In addition to what happyhedgehog says, please see a lawyer.
Here is why:
The home he is asking you to remortgage and take equity from is your marital home. It is a joint asset.
The equity he will use to buy a new home - unless he buys it in both your names- will be his, as he bought it when you were separated.
Therefore, he will have a claim on the marital home, but you won’t have a claim on the new place, without arguing it out legally.
Before you re-mortgage, you need to be clear about who owns what, and who pays for what. If he wants the new place as his, you need him to sign the marital home over to you, before you re-mortgage and release the equity to him. All of this needs legal advice and legal documentation.
Buying a new place has a permanence to it which renting does not. Therefore you need to make sure that your interests are protected.
Mental illness is an illness like any other. I am struck by the fact you say you have intrusive thoughts. If they are caused by previous trauma, then your reactions and behaviour are a response to that, and the right support and therapy will help.
But aside from normal parenting anxieties around potential neurological diversity and mobility problems, what is his evidence that this has harmed your DD? Because that is what he needs in law for it to be visitation only.
Please, please see a lawyer after your GP. You do not need to tell your H you have taken legal advice. The lawyer will help you understand your position.
What RL support do you have? You could contact Rights of Women who will direct you to support organisations.
I know you desperately want things to be okay, and you are blaming yourself, but you need to protect your interests. Chloris upthread is correct, your DD will want her normal routine and her mum.
All the best