The father already has financial commitments to his existing children. If he is to continue to provide them with a stable home/roof over their heads as part of a co-parenting set up, he is not in a position to 'share his worldly goods' with another adult. With this in mind, the most he can offer the OP in terms security relating to housing, is rent free accommodation in his house.
Understandably, this isn't enough for the OP, as she wants to be able to have the same housing security that the father benefits from. However, this isn't something the father feels willing to provide, for legitimate reasons.
The father agreed to have children, making it clear that he wouldn't relinquish and equity in his home. His intention was to provide a roof over the heads of the OP and the baby, but it would remain his. At the time of choosing to get pregnant, this seemed agreeable to both.
Upon becoming pregnant, OP - unsurprisingly- had a change of heart. A dynamic where your only option of a roof over your head requires the benevolence of a home owner to grant to permission to stay is very different prospect when you have a job and no responsibilities for providing for anyone other than yourself than when you are heavily pregnant, or breastfeeding or have a baby to provide for.
I don't think either OP or the father of the baby have acted 'in bad faith'. I think their motivation for wanting what they each want is driven by the same interests as they both want long term security of housing for themselves and their children.
If they can see this, and understand each others motivations, this will provide a better foundation for finding ways forward. There isn't an easy or readily available solution, but they need to work on one that allows the new person who is coming in to the world to have the best chance of a good life - which entails having strong and loving bonds with both parents.