Hi Duda,
I do not wish to add fuel to your upset but “playing devil’s advocate” it seems there are two issues:
1. You finding yourself a new home
2. You being able to look after your child
I do not know if this helps in any way but do not forget that the child is jointly yours and your partners and I suspect he would find coping with your child alone would cause him to struggle. This might be a bargaining tool. The responsibility should be shared. Talk to him.
My first wife left me over a Chinese meal and took my son with her. It nearly broke me. I wish she had just sat down with me and talked about what her needs were. Men can be stupid, but also complacent when you have a child since they subconsciously assume you are more tied down. If he realises how serious you are about leaving and what his responsibilities are he might treat you better…having said that I also think that sometimes women’s expectations rise after giving birth… I suspect he might simply be behaving as he did before the birth and needs time ( or telling!) to adjust.
.