There are pros and cons to both imo. If you rent in the private sector, you can be given notice at almost any time and have the stress of finding somewhere affordable to live in an area that's convenient for schools, work etc. If you lose your jobs or become too unwell to work, your rent will mostly be covered by benefits, your mortgage won't.
Owning gives you more flexibility and choice, and you can downsize on retirement to reduce your outgoings. And you have something to leave your children. But my god, the cost and headache of maintaining it! I've had a new boiler every 10 years, on average, new fencing, had to replace windows/doors, guttering etc, bathroom, kitchen and the bloody place needs decorating all through now. I'm on my own due to bereavement and still working nearly a year after retirement just paying the bloody bills.
I sometimes look at my MIL, rent and council tax paid by benefits, who's had her windows replaced, a new kitchen, bathroom and heating system all done and paid for by the council in the last 10 years and wondered if it's worth the hassles of owning.
@Ilikewinter, I'm really surprised your DM can't get social housing. Housing for older people usually has a high turnover and becomes available fairly regularly. And she'd be in priority need because of her age. The councils in my area would definitely help and she wouldn't have to wait long.