See if someone else will reply with the average amount they are spending on a car all in (vehicle/COE, petrol, road fees, parking, insurance, etc). I have a guess but it's just a guess.
Grab ect one way half-way across the island can be S$ high-teens to low-$20s. Usually, you can't go very far without paying at least $10. So you can figure out per working/school day what you need and then some buffer for entertainment on the weekend (or take public then when not in a hurry). If it is raining, waiting time can be a bit more and prices can jump but if you set your mindset that there's "nothing one can do" it is OK.
You can consider is find a place that is more convenient to/from pubic transport. Try to get closer to MRT vs. having to transfer on a bus (waiting time is the biggest constraint). One thing is that "not far" from the MRT or public transport is sometimes "not exactly short" or "very quick" in the heat of the day or the middle of a down pour. With kids, it becomes even more of a challenge. I'd also look for whether there are covered walkways from MRT to home and test out the routes at the time you will be going (especially the routes the kids need to take, some directions can be very crowded at peak times and not easy to manage with little kids).
Of course, for many here a car is a luxury and it is definitely not needed, so as you say you can test it out for a few months and then decide whether to stick with it or get a car. One constraint is that the housing will likely be fixed for a year or two, so some of the above impacts how easy or difficult it is.