Homeless with 2 kids (one is a baby)

My husband and I have been going through a lot. He doesn't accept my child (he has one too) and we just had one of our own. 
I've tried taking him to family counseling but it was no help. 
He has never been abusive to my child, he literally just ignores his existence. 
It's not the first time we had a big fight and he told me to leave (being that I have no family in the US and I have nothing to go back to and I just had a baby).
Before any of you go on about how I shouldn't have married him I'd like to say he wasn't like that when we met over 10 years and when we decided to be together he knew I had a kid and he was nice to him. 
So right now I'm just looking for a shelter to be with my children and get back on track. 
I'm doing some research about it but I have no clue how to start and what happens next. 
So if anyone who has been through this or has any advice to share that would be very nice. 
I'm in New York. 
I'm already beat up emotionally so please just ignore this if you can't give me useful advice. 
I just need to know where to start and what's to expect in finding a shelter for me and my children.