Thailand with 2 little kids in May

i love bangkok and could easily spend much longer than 4 nights there, but you are travelling in may (it will be hot), and with kids, and its a huge city and as you will have 1-2 days more there at the end of your trip, 4 nights at the beginning are probably enough. i would definitely choose a accommodation with a pool. there is no "best area" to stay in bangkok, i'm sure you can ask 5 people and get 5 different answers. personally i dont really like the sukhumvit area, i prefer to stay on the river in banglampoo (near kao san road). wherever you stay in bangkok, you want either to be close to a skytrain station or close to the river, where you have access to the chao praya express boats, for me a very nice, jam free and breezy way to get around bangkok. even if you dont stay near the river, i would definitely take a trip on a chao praya express boat (basically a bus on the water), its cheap, there is plenty to observe on the river shore, and should also be good fun for your kids as well. you can for example take the boat up north to nonthanburi (about 1 hour from banglampuu), and there you could take (or charter) a small boat to discover the klongs. bangkok is also a great place to treat yourself (and your wife and kids) to a massage, or get a pedicure, or a facial etc. and of course, plenty of beautiful temples, amazing food, loads of shopping possibilities etc.

if you go to ayuttaya, do it as a day trip. the old and new ayuttaya are "mixed together" and its totally worth visiting. on the other hand, there is so much to do and see in bangkok, and also you will probably need some relax time after the flight... no need to decide before you are there. if you feel like going, take the train and enjoy a day there.

kanchaburi is a very nice place, its a only a short trip away from bangkok and offers a lot. also, its very relaxed and set in beautiful nature. the activities / sights you are looking look good. i have to admit that i'm not sure about the water levels in may at erewan falls (if there is "enough" water or not). if yes, i would definitely go there, the falls are beautiful, you can swim in some of the pools.

i havent been to salad beach on koh phangan, so cant comment on that. i've been to thong nai pan beach and really liked it. the beach is beautiful, and great for kids as its totally wave-free and very shallow, so very safe for them to swim. but yes, no snorkelling. my brother and his family (with 2 girls, then 7 and 5 years old) stayed at buri rasa last february and they really loved it.

chiang mai is a great place, and a week there would be totally right. but may is indeed not the best time to go to chiang mai. mind you, it will not be cooler in bangkok :-).

Some random thoughts...
May is not busy, you don't need to pre-book anywhere. Very easy to book just the day before on any of the popular booking sites.

Far less hassle and more comfortable to book the coach / ferry combo to Koh Tao with Lomprayah (http://www.lomprayah.com/ww/E/index.htm). Leaves Bangkok at about 6am and gets to Tao early afternoon. Comfortable coach and fast catamaran. Unless you want to stay with / near your friend, there are much nicer stretches of beach than at Clear View resort. It's quite near the pier.

Haad Salad is nice, the beach is not very long, only about 600m with several resorts next to one another. Other resorts have bigger pools than Salad Hut which might be something to consider with kids. You could easily book just 1 night and look when you get there. I was last on Koh Tao and Phangan Haad Salad last May and the sea was shallow but there are deeper pools here and there. You have to get out past the house reef to see anything of interest snorkelling which might be a bit of a stretch for a 4 year old. Snorkelling is far more spectacular on Tao with lots of bays where interesting stuff is quite near the shore.

Ayutthaya just for a day trip is a bit of a shame. Without small kids you can keep running all day and see quite alot of it but I doubt the kids will put up with that. The seafood restaurants along the river are really nice on an evening and to sample those you'd really have to stay a night.

if we find a trustworthy babysitting service

Not sure how you would determine whether or not they are trustworthy.

I must be an over-protective parent, which I really try hard not to be. But for the life of me I can't even imagine leaving my 4 year old with a stranger in a foreign country. The thought gives me chills. And I'm the one who is usually rolling my eyes at other parents and calling them paranoid. But leaving my kid with a stranger in Thailand? Not a chance.

To find a babysitter, maybe see if there is a nursery/ day care center and ask there. The Thai wife of an English expat friend of ours on Koh Samui works in a nursery by day and in the evenings does freelance babysitting if asked by a parent.

but generally I guess 4 nights is about right?
For a superficial scan, yes. I could spend a month in Bkk and not see everything.

hotel in an area close to the main sights (a colleague told us the best area would be near Sukhumvit - true or false?),
Only if you like looking at hookers. Sukhumvit is hooker central ( but only at night ).
However, it is good to be near the skytrain, as that is best way to get around Bkk. If you get a place further east than Asoke, you will spare your kids an education you may not want them to see, LOL.
There is no skytrain to the Grand Palace area, which is where most of the "sights" are located.

I can't imagine trying to drag a 20 month old around the sights in Thailand- push chairs are useless outside shopping malls and Thais just don't use them.
It will be very very very hot. Take precautions with the kids. Also for mosquitoes. There is no prophylaxis for dengue, which is transmitted in daylight hours.
Day trip to Ayutthaya is enough. IMO if you go on a package tour it will be 100% easier with the kids.

How and when do I need to buy the night train sleeper tickets?
Buy from advance ticket office in Hua Lumpung railway station as soon as possible after arriving in Thailand.
Don't let a tout con you into going to a "TAT" office. TAT doesn't sell tickets, to anything.
You can change them up to an hour before departure for a fee. I've even got a refund after the train left, but I wouldn't count on that normally.

I would love the freedom of just going with the flow .
I wouldn't even consider prebooking in May. One person stays with the kids and bags in a restaurant while other looks around for a place.
Perhaps prebooking in Bkk would be a good idea though. It's just too big to look around if you have no idea where to stay.

if we find a trustworthy babysitting service,
LOL. I'm with Jack on that.
Are you 100% certain you want to take them with you? The boy won't remember the trip. Even if you just took the girl it would make your life a zillion % easier as she can walk.

it seems that at that time of the year (mid May) it is unbearably hot there
Nowhere near May and it's already "unbearably hot". However, that applies everywhere, so don't think that because it's in Kanchanaburi or the islands that it will be less hot than Chiang Mai.
Check this out https://www.youtube.com/watch?v=Erf2iFHG44M
The relevant bit is at 2 minutes 55 seconds. Always good for a laugh anyway.

Was thinking Salad Beach, as it seems you can do some great snorkeling there right from the beach (so hoping of taking the 4-year old and showing her some of the underwater world) and the accomodation I found ("Salad Hut") has good reviews. However I read the water is too low here to swim??
That's confusing. The beach is small, so either it's deep enough to snorkel, or the water is too low to swim over the whole beach.
When I was there I didn't see anyone snorkeling.
Be advised there have been box jellyfish attacks in Thailand and are you sure you want to expose your kids to that risk? There is a thread on TT about it if you search.
Don't expect much in the way of emergency care on the islands ( possibly Samui might be OK ). Thailand is definitely third world when it comes to public health care. Take really good insurance so you can get treated in a private hospital if necessary.

i've been to thong nai pan beach and really liked it.
????????? Which one, Yai or Noi? A VAST difference between the two.

just a tip for the train. Only book 2 berths-- they are big enough the children can share with you. As for something for the youngest, look at something like a mountain buggy. They were originally designed in NZ to go over all terrain. Other than that, you see plenty of Europeans around with small children and some sort of buggy/stroller/push chair. Heck, I've recently seen 2 guys in different wheelchair types here on Koh samui. Neither seemed to be impeded in any way.

Dont forget some see the glass as half empty others as the glass half full.