This would be an excellent question for Ask an Apologist. I will give you an answer from what I understand, and I am not well versed in Catholicism – I am hoping that my comment will prompt discussion that leads to a more exhaustive answer.
The Catholic Church recognizes the Baptisms of Children outside of the Catholic Church as valid. Likewise, if you left the Catholic Church and were married outside of the Church after 1983? – your marriage is also considered valid.
Anyways, I believe, your child can receive first Communion at the Catholic Church if you begin raising your child as Catholic and send them to all of the classes that are required before first communion. If you are not going to raise your children as Catholic individuals – then the answer is “no” for the most part. There are exceptions that can be made for individuals outside of the Catholic Church so that they can receive communion in extraordinary and dire circumstances, but this is not one of them.
I do have to say that if you consider yourself Catholic at this time and you have chosen to raise your children outside of the Church you may be in hot water. Likewise, if you are currently Catholic and were married outside of the Church you are definitely in hot water and should look into getting your marriage convalidated. <- I think that that is the process that I am looking for…