You know what, you are his mom. I understand why they are saying what they are saying, however, I also understand why you are doing what you are doing. Question, can he stay at any shelter or anywhere else instead?
Ultimately it's your choice what you want to do. It's great you are getting help. Don't let other people make you feel to blame b/c you definitely are not. If he were to say with his father that would be even more enabling. It's a lot easier to say leave them out in the cold when it's not their child. I cannot even imagine.
Tight, tight hugs to you.