OK, I have a bit more information now. As an Irish national, your MIL has a right to settle in Britain. However, as she hasn't lived in an EU country for some time, there are restrictions on what she can claim as she would fail the habitual residence test.
If you can bring her here and have her live with you for a few months, she could probably pass the habitual residence test and then be in a position to claim income support - although this is means-tested and her pension would be taken into account. An alternative is to bring her here as your dependant and then claim that you cannot afford to support her. Accommodation-wise, she would have a better chance of obtaining local authority or housing association housing if she has some health problems. Housing is allocated on a points system and points are awarded for a range of criteria. Health problems and children get the most points, so health would be her best bet.
If she cannot get LA housing, she could look into privately rented accommodation with a view to obtaining housing benefit. She could ask for a pre-tenancy determination, which is where she and her prospective landlord fill in a form, send it to the rent officer who decides how much (sometimes all) of the rent is eligible for housing benefit. That way, she knows that she can afford the property as she knows how much of the rent will be covered by housing benefit. Two disadvantages are that (a) the landlord knows she will need HB (and some can be difficult about that) and (b) the process takes about 2 weeks, during which time the property can be let to someone else.
Let me know if you need anything else.
Oh and do check that her current pension can follow her abroad.