I wouldn't risk it. Say the aircraft pulls onto it's gate on time, it still takes a minute or two to get the doors open. Then you have to get off, and if you are booked on the same airline the whole way and have checked all the way through to your destination, make your way to the flight connection desk, pick up the information about your onward flight (gate location and how to get there, etc,) and make it to your next gate. This might be close by, but equally it could be a tram, train, monorail or bus transfer to another satellite terminal or even just a very long walk. If you are not there by 'gate close' time, usually 10-15 minutes before the scheduled departure time, they will start to look for your bags. However, even if everything has been running to time so far it is unlikely your bags will have made it through to the onward flight. There simply isn't the capacity to get bags off one flight, across an airport, and onto another flight in less than 35 minutes.
If you are on a different carrier you will probably have to clear customs and immigration, collect your bags and check back in and renegotiate security again. There really is not enough time to do this. The minute one thing doesn't go according to plan you will start to pick up knock on delays and have no chance at all.
I'm a very experienced traveller and know many of the world's major airports and the way they work well enough to be confident of a speedy passage through an airport, but I wouldn't do it alone. I especially wouldn't do it with a toddler and baby.
As for flights waiting, I don't know if this was people's experience from some years ago, but I am not permitted to wait for individual passengers, or even groups of passengers (I'm a long haul pilot.) The complexities of slots to take off, land and cross different country's airspace, parking stand allocations, ground staff availability, and more mean that flights run on a very tight schedule. A couple of minutes delay in one place may mean they miss their slot and fall far behind schedule. General airline policy is to attempt to stick to the schedule at all costs - punctuality is most airline's second priority after safety.