I agree with myrtle.
What I understand from your posts, op, is that you are looking at a situation where, if you move to your father's house, you will have no housing costs over the duration.
This would be a saving of at least £6000 a year (or whatever annual rent you pay, but I've gone for the base minimum here for private rentals ). Over three years, with this minimum, you are looking at a saving of £18000 - - that's a year's take home pay for something on a slightly higher than average salary.
This is substantial money. It's a situation most people dream about. It would give you a level of financial freedom that would significantly expand the possibilities open to your and your child.
For your dp to turn away from this suggests he's just not in tune with reality, nor does he think in the medium to long term about the financial stability and security of either himself or his soon to be family.
In many respects, it would be valid to argue that, in light of this housing offer, his demand to live close to his mother now incurs a cost of £6000+ a year.
I am going to say something very generalised here, but, in my experience, I've found that a lot of men don't really understand that life stages require change: in environment, in relationships, in values, in perspectives. I know so many men who seemed to get psychologically stuck somewhere in their twenties and just stayed there, despite the circumstances of their lives changing dramatically over the ensuing years (with partners, children etc).
I suspect, op, that you may have a problem with this with your dp. It seems clear that his relationship with his mother has not evolved over his twenties, and even in the face of impending fatherhood, there are no signs of change.