You would want to be certain you could get the price you think you can.
Even if you put it on the market today, it may not sell till next Spring and another 50k could be gone off the price.
Also, moving with 3 children is a very, very large upheaval.
The older they are, the harder it is on them.
You would want to be certain that the rented house you get is not, and won't be, up for sale in the near future. There is nothing worse than getting the call from the landlord/agency saying 'you have to be out in 6 weeks, sorry'.
Will you have the job security/savings say in 2 or 3 years to buy another house...
We are currently renting, but we have substantial savings to buy another house when it comes along.
The whole idea of owning your own house is - that you like living there, can afford it, and it provides security.
It's a whole different ballgame not being able to paint the kids rooms, put up a picture on someone else's wall etc.
Renting another house with little or no savings for another deposit may not be a great idea. You may end up spending the 'extra' money every month anyway.