If my tax returns got rejected with code IND-507, but no one else has claim to our son as a dependent, should I include proof of his identity when I file by mail?

You don't have to.  If someone else has created a fraudulent return using your son then you can just file your correct return and the IRS will see that he's been claimed by you on past returns and it will be fine.  They will almost certainly issue him a five digit identity protection pin number to be put on any tax return he's on going forward.  But if you would like to throw a copy of his birth certificate in there it certainly can't hurt provided the parents named on the birth certificate are the ones claiming him.

Hello,

I am in this same situation. One of my dependants was claimed when the other parent was not current on child support and without a form 8332 from me. Do you suggest that I include this information with my paper-filed tax return? Is there anything else that I should include at this time such as the court order, parenting plan etc? Thank you so much.

As mentioned by @RobertB4444, none of that is necessary.  You can choose to supply the information if you wish, and that may speed up the process somewhat.  But what the IRS will most want to see is that the child is your qualifying child:  that they are a blood relative (if a son or daughter, this is resolved with a birth certificate showing that you are the parent), and documentation that shows they live with you.  If last year there was an 8332 filed, it might be worthwhile to file an 8332 that revokes the authorization that might be on the prior form.  But if there was no authorization for this year, technically it is not necessary to do that either.

These are the tax questions involved.  For any legal issues you would need to contact an attorney.

do not attach extraneous material unless the IRA contacts you and asks for it.

IRS will resolve conflicting tax returns in its own way on its own schedule.