We did something similar in the uk. We sold our flat and moved with a 4 week old and toddler into rented, the moved again into a house we bought 2 months later. We has found the house before we sold the flat, but had to break the chain to keep everything moving.
I would say this - moving into rented was easy easy easy. No need to buy soft furnishings, decorate, sort things out properly, if something breaks you call the landlord, and whilst its more expensive you know there will be no nasty shocks (fork out for new boiler, pipe burst etc).
Moving into a new home (that you own) proved substantially more stressful! Burst pipes, broken dishwasher, blocked drains all in the first few weeks!!! Still sorting out insurance claims 4 months on.
Also our toddler had a lot of change in a short time (new sibling, new house, new park) and was very unsettled for a month or so, which wasn't easy with all the other stuff I had to deal with.
I would do it all again though. We desperately needed more space, and we got a fab house in a lovely area. It's hard selling and buying at the same time and we found it does simplify things to sell first then buy later.
Good luck!