I really want so say I feel badly about your situation and give you a
as I'm sure you could use another one.
In response to finding a new place to live, another option would be Nutley/Bloomfield/Belleville. I know Nutley has buses to NYC and I believe the others do too. The rent is within your price range for a 2 bedroom (my mom's friend is paying around $1200 for a 2 bedroom) and is pretty close to the city so the commute wouldn't be too bad. It's also a nice, safe town for your kids (the kids still walk home for lunch!) and there are plenty of small stores/restaurants/etc. where you could get a part time job when you're ready.
About your husband's behavior, I can somewhat sympathize. My husband has never fed our daughter, gotten up with her at night (well, once by force for about 3 minutes till I took over), 'baby-sat' her, or bathed her. He has changed a few diapers and outfits, but only if I tell him to, he never takes it upon himself to do those things and when I ask him he'll do it with a sigh or eyeroll. It's not that he doesn't love our daughter, cause he really does, but he feels that's my job, so maybe your husband thinks that way too? Like another poster said, it could be old fashioned thinking that he works outside the home and you work with the baby at home so he's your responsibility. But to really know if he thinks that, or if it's just that he isn't interested in his kids, you'd have to see how he acts with your son aside from caring for him. What I mean is, does he come home eager to play with your son and happy to see him and you, or does he not even acknowledge your presence? That would make a big difference to me regarding whether or not I'd stay with him because if he's not happy to see your and your son now, he probably won't change. Unfortunately, since he is playing video games on his day off and not 'peek a boo' I'm thinking he might just be too wrapped up in himself to worry about you or the kids. My husband doesn't have any video games, but I know if he did and sat playing them I'd get very irritated that he has his 'day off' yet I work 7 days a week (I'm also a SAHM). Luckily for me though he's not bad on the weekends and will play with our daughter (still not feed her or things liek that) so I do get somewhat of a break. Yeah, I'm still in the house as he'd freak out if he had to watch her by himself, but at least she has someone else to entertain her so I can do other things. If you can get him to move in that direction it will be a huge help for you, but he's only going to do it if he wants to.
I can sort of see staying with him though, at least temporarily, because at least you have the benefit of his salary and either way you're taking care of 2 kids by yourself. Once the new one is born and you're able to organize yourself and how your care for them maybe it will be easier for you to see all your options. If you get a part time job, or even a full time job if you can find cheaper childcare (which I know is hard), then maybe you'll feel more secure and can better evaluate where your relationship stands and if it's improving or not.
The money thing is also tough, and without those issues I'm sure things would be a bit better for you. We also have those issues since I'm a SAHM and my husband is in medical school. For us though, it's not as bad, since we know there's an end in sight once my husband finishes his residency and we pay off all our loans, but for now we live on loans and money from my mom, which is hard. My husband often works from 5am-8pm (and is on call overnight at the hospital for 36 hours at a time twice a week) so I'm the full time caregiver too. In fact, until my daughter was about 7 months old, she'd cry when my husband picked her up! But she likes him much more now and gets very happy when he comes home and that has made him want to interact with her more. So look at how your PJ interacts with your husband because if he's a bit afraid or cautious with him it might make your husband less likely to bother with him. I know my BIL was like that with my nephew as an infant, always handing him back to SIL because he 'didn't want' his father. Well, yeah, he didn't, cause he knew his father was afraid of him and his mom was much more comfortable.
We sorta planned our daughter, but 'planned' that she'd be born around now, but instead she turned 11 months old today, so sorta not predicted and I know how that feels, but I could never have considered adoption and if we found out we were having #2 now I couldn't think about it with that one either. I am also expected to do things like find a new home for us, all that stuff (we sorta shut down moving for the time being though since our daugter sleeps with us anyway so we don't need a 2 bedroom yet), and my husband feels that since he's gone all day that I should be doing these things while I'm home, so I can empathize, and want to let you know that you're not the only one out there.
I really hope things start to look up for you and your family soon.
even more you can NOT do. 
