The Church makes allowances for a Catholic marrying a non-Catholic called a dispensation from form. If your wife had done so, your marriage would have been perfectly valid with no problem.
Since she did not, this can be taken care of through what is called convalidation (and maybe even a process called radical sanation). Your wife needs to speak to her priest.
The problem is that she did not do what needed to be done from the Catholic standpoint, clearly she didn’t ask about it-- a lot of people don’t. It can all be resolved fairly easily.
I think though, that we could not, well, I could not, assure a priest that he will be raised Catholic. While I don’t see the harm in a baptism, and do want my wife to be happy, I wouldn’t lie to have it done.
Our marriage has been complicated from the start, not just with religious differences but cultural also, whereas I don’t feel any harm will come, I can comprimise.
While we have attended Mass a few times, she has no paticular church she attends regulary and I don’t believe she speaks to Priests as a general rule. (previous issues) She does attend my church occasionally also, at my request.
I know the above would cause issues in our parish. Parents must attend a baptism class and if they have not been members for at least 6 months they are asked to provide a letter from their previous pastor or someone who knows them well stating at least one parent is a practicing Catholic in good standing. A similar letter is required for the child’s godparents if they are not members of the parish.
To the OP, the biggest concern is if your wife want to baptize your child purely for “cultural” reasons. In other words if she feels it is important just because she was raised Catholic, but that she does not believe the Catholic faith and therefore will not pass that faith on then to what reason would the sacrament be conferred? This is the same reason that at least on godparent is required to be a practicing Catholic. They are charged with raising the child in the Catholic faith if their parents are unable to.
To be honest, I’m not sure. I do know she believes in baptisim for infants and the Catholic faith and wants to do it for the sake of our son. If I didn’t think she did, and just wanted to do it for the sake of tradition, I would probably be more proned to dismiss the idea.
We have discussed how we will raise our child. It’s been a point of contention at times. For me, my beliefs are non-negotiable. I can’t reconcile them with the Catholic belief system. While my wife does attend church with me (and vice versa) she has never backed down from what she believes either. I respect her for that. I guess my point is, that our son will be raised with both of our point of views. Thus, I believe a Priest, would not be too comfortable with the idea of baptisim if it is necasarry for him to know the child will be raised catholic.