My husband and I share joint custody of our two year old son. His family has been telling me that he is not spending time with him. His 75 year old grandmother is caring for him the weeks he is with his father. Im also 7 months pregnant with our second child whom he wants nothing to do with. He doesn't want him to know he's the father. But he wants to continue to keep joint custody of our two year old. My question is what can I do about getting custody of the two year old and getting help finanically from there father?

Go back to court and ask for the joint custody to be admended and child support ordered, you could wait to the 2nd is born, and do a court order for both.

If he doesn't want anything to do with the second child will a judge allow him to continue joint custody with the two year old, and have nothing to do with the second?

Well first off, I'm confused. You said "my husband and I share joint custody"... are you still married?
If so, I may be wrong, but I would think your divorce would have to be final before any custody issues were put in place.
So if you are still married, is this custody something you have worked out between each other, or is it court ordered?

Or did you mean to said "ex" husband?

If there is a court order for custody you just need to file a petition for a custody change, then it is up to the judge. As Chuck said, and I agree, you are so close to having the second child, if I were you, I would wait until that child is born then have custody and child support for both children be heard at the same time.

That way it saves you time and money.

Whether he wants to have anything to do with the child or not is not entirely up to him. He is fathering the child therefore he has a responsibility towards the child.

He can not exercise any custody or visitation rights he has, but he still needs to support the child. Nor can he deny the child the knowledge of who its father is.

I agree with the others. Wait for the 2nd child to be born, then file for custody and support for both.