Buy a flat or house whatever you can, if its really not enough, put it into savings account, move in with your mum, save like mad then buy.....
I am a Landlady and know how difficult it becomes to get on the housing ladder with children, however hard it is now it will just get much harder.
Better to only get a 2 bed house of flat now, dcs can share for 10 years whilst you save for a bigger home.
Two things to remember,
one, rents go up over time, morgages don't, in real terms they reduce.(Try and secure a 5 yr fixed rate to give you security of knowing the costs.)
Secondly, you have no security renting especially when your dcs start school, you will want to stay put and not be constantly worried about your Landlord not renewing your tenancy every year.
Re car, put up with a basic car, cars waste a fortune in depreciation, all they need to be is cheap to run, and cheap to insure and repair.Doesn't matter beyond that.
Pay down any debt that costs you more than 3% interest, out of the money you save staying with your mum.
This inheritance has given you a wonderful opportunity to change your future to get a secure home, don't spend it on anything else!