Hi,
We find Bangkok a little tricky with our young ones (went when they were 2, 4 and 5) but a few things I would definitely recommend to make your stay fun for everyone:
-If you're in a large hotel, make sure it's got the 2 double bed set up and if possible, some sort of balcony. We also love to sit and talk (ie have a glass or two of wine) long after the kids are asleep, and this makes it possible. When we haven't had one, we sit outside the door in the corridor, door slightly ajar and ignore the strange looks from passing guests! (Makes for interesting people watching though!)
-If you can be near a supermarket with groceries (including international if you're lucky) this would be a good way to easily get the foods your little ones might be craving (bread, jam, etc). And your hotel should have a small refrigerator too. We do this in Bangkok and keep the fridge full of yoghurts, milks, juices, vegies and other healthy things we don't want them to go without, and that they can snack on.
-A pool is almost essential - if you're in an otherwise-boring large hotel anyway. Hours of entertainment on very hot days.
-Another possibility is to see if you can find the sort of hotel (even a small hotel or guesthouse if you're up for it) which has a family-style atmosphere. I know backpacker accommodation's not what you're after, but I do remember quiet, small family-run guesthouses with meandering pets, homecooked meals and a common courtyard, cheap enough that you could take 2 rooms, not to mention sit in the courtyard/area just outside the rooms in the evening while the kids are asleep. I'd personally not consider the baby alarm thing.
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Or, like another poster suggested, probably the best solution would be to see if you can find long-term accommodation. We did this in China in 2009 - rented a furnished apartment for 3 months. We used a middleman (agent) so paid double what a local or expat might have paid, but it was still incredibly inexpensive by Western standards, and we still spent less than if we'd been at home... it was easy, simple, and the place was set up ready for us when we arrived. We just googled/researched. You could ask on some of the online expat forums (there are a few in Thailand).
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Finally, take a fold-up stroller for your 2yr old (we found it a lifesaver when our twins were 2 and the heat wiped them out in less than 5 minutes!) and a portable dvd player - the kind with cables you can attach to the back of the tv and play a dvd through. Also rechargeable batteries, a charger and an adaptor. Crucial for our twins travelling at 4 and 5, and we anticipate this year at 6 too. You can take this anywhere and keep them happy, especially good on planes. We've even done the odd hotel cocktail happy hour with kids quietly watching Disney and sipping juice!
Good luck and have fun!
