My husband and I have an invalid marriage in the eyes of the church as we were married in a courthouse. I am Catholic (Confirmed and practicing) my husband was baptized Assembly of God and is now non-denominational and was previously married (no annulment). He is also active duty military and we are stationed in California, so I had to move away from my parish in Texas. I have not become an offical member of any church out here so I went to the base chapel and spoke with the Father there about baptizing my son. He insisted that we could do begin to talk about his baptisim until 1. my husband started the annulment process and 2. we go through the Convalidation process. After all my research online, I could not find any churches that listed those as prerequisites. I was under the impression that for the licit baptism the lawful parent or guardians give consent and there is founded hope. If we are both consenting to the baptism and to raise him Catholic, why are they denying us this rite? We take no issue in going through this processes to fix our situation, but to deny my son while the annulment process plays out seems unfair.
The matter is not entirely black and white. Canon Law merely requires a founded hope that the infant will be brought up in the Catholic religion (Can. 868 §1, 2). Not being in a valid marriage does not dash any hope that the child will be raised Catholic. There are plenty of Catholics in invalid marriages who attend Mass regularly and raise their children Catholic. However it does generally raise the question of whether someone who is living outside the rules of the Church would raise a family within the Church. Most of the time after talking about the matter the child will be baptized.
I recommend you find a priest or parish where you feel comfortable and discuss the matter with them. Of course, I would also recommend that you regularize your marriage with the Church but that is a separate matter that should not affect the baptism of your child.