what you actually do for a living wont really have any bearing on whether you can get a mortgage: any lender will look at your ability to pay back a sum that they have lent you. i make the assumption that from what you say in your post you are both not working because you are looking after the children together?
If this is the case it makes it much harder to get a mortgage, especially if you have no income or savings. If you own your own property, i dont think you would get any housing benefit, so again, making the assumption that you get this already, that will immediatey be less income for you. Havingsaid all that, mortgage lenders seem to want to lend to anyone these days (not meaning you are just anyone, of course you are not, but meaning no matter what their circumstances) so there is no harm or loss in approaching a mortgage brokr to talk through the posibilities. You need to check you do have the right to buy first as some council properties are exempt, for example those built to house disabled people