Surely you can see that from XW's point of view, getting her boyfriend involved - financially - would be an unwise move?
Say she just needed the £4K deposit to buy your husband out and her boyfriend offered her that, genuinely no strings attached and she was certain it wouldn't affect the balance of their relationship or ever be thrown back her. Happy days!
Except... it isn't just about £4K, she also needs to be approved to remortgage in her sole name. So actually, that's not a magic solution. If it was just about finding £4K then your husband could give that up and all is done.
Her remortgaging jointly with her boyfriend to be approved?
Imagine the MN advice, in this situation. I'll summarise the responses for you: HELL NO.
He's her boyfriend. She has no security of that relationship no longer how long they've been together. She'd be swapping potentially owning* all the house, for boyfriend having a legally defined share.
*she sounds like she has a great case for the majority or all of it vs your husband based on what she herself has actually paid, her earnings, and potential, her position back then as primary carer, the balance with his other assets such as his pension, and yes - the fact that he is married to you and therefore your presence, if not your actual £savings - would be considered when looking at his financial needs.
Her boyfriend would get hit for 3% SDLT potentially depending how they did it - just a joint remortgage, I believe he'd get hit.
There's every possibility that he wouldn't be able to jointly remortgage with her - because he has his own mortgage. Ditto guarantor.
What if he gifted a larger amount of money to allow her a smaller mortgage that she could be approved for? Well, firstly they're not married so he'd be a fool to do that! And if it was loaned, he'd want a charge on the house. But he'd have the third charge (mortgage, secured loan, him) and the mortgage company can refuse that.
Plus, even if he had a loan with a charge - if it went tits up then that's him into paying solicitors and forcing a sale!
There are just a few of the reasons where instead of complaining that her boyfriend should get involved, you should understand that from both their points of view, it really is better if he doesn't.