We're driving along the Garden Route, from PE to CT, with 2 young kids (5 & 3). We plan to take about a week (It's a 2 week trip, we have 3 nights in a game lodge near PE and plan on about 4 nights in CT.)
My question: Is it better to base ourselves at maybe 2 places along the Garden Route and do daytrips, or stay in a different place every night? If the former, which places?

It depends what you want to do on your day trips and how accommodating your kids are with regard to car time. I would recommend going for a different place every night, take maybe two nights in Knysna (just because it's central so that gives you time to catch up with yourselves).
Our kids are now 5 and 8 and we have holidayed on the Garden Route once or twice a year ever since our oldest was born. Here are our favourite places to stay along it.
In George our kids love the Railway Museum.
Do the day trails from Ebb and Flow in Wilderness if you like hiking. (they are short trails, a couple of hours with the kids, we did them with ours about 2 years old)
Take the Featherbed Ferry trip in Knysna.
Make a stop at Noetzie (between Knysna and Plett) to enjoy the beach below the 'castles'.
Monkeyland is a great visit while you are in Nature's Valley, as is the Elephant sanctuary. And walk to the suspension bridge at Storms River mouth and take the boat ride up the river.
Have fun!
I agree, keep moving slowly eastwards (or westwards i guess... depends which direction you're going). There are lots of places to stop along the way and I for one wouldn't want to keep back tracking.
When r you going? School holidays here would make things a bit more difficult, to be impulsive - like booking the featherbed cruise or getting accommodation with short notice etc., as it gets very full in that region over school holidays.
At Stanford (small village near Hermanus) you can take the family for a picnic at Klein River Cheese farm.
In Cape Town, the Two Oceans aquarium is really nice for the whole family, kids will love it.
I second Knysna - loved Noetzie, very atmospheric (but lots of steps down, good exercise : ))
Note that the Tsitsikamma suspension bridge is currently out of bounds undergoing repairs following a fire earlier this year - I'm trying to get updates here. Boat trips have apparently already restarted though.
PnP.