It''s not possible for your father to unilaterally take your mother''s name off the deeds. He also can''t unilaterally transfer it to you and your brother as she has to agree to this. She is still a co-owner with all the rights that brings and it could be argued that she left the property with your father as an investment or to make things easier for him - as many people do if they leave someone who is caring for the children in jointly held property. Usually, though, this is part of a Consent Order on divorce and there is a ''trigger point'' at which they get their money.
Presumably one reason why your mother agreed to equity release on her partner''s home was that she was relying on the security of her co-ownership of the house with your father - so that she would have something in the event of her partner''s death. Moving back with your father seems a bit drastic but she does need to have something.
Really both your parents need the closure and security of a formal divorce with a financial settlement. Even though your mother has been gone a long time she still has ownership rights in the house and your father will need to meet these. Equally, she doesn''t have the right to move back in unless he invites her.
How big is the property, and how much equity does it have? Could it be sold and both of them have enough to buy somewhere smaller to live?