Religious Ceremony After Civil Ceremony

[Phx Mom]

My hubby and I just found out a couple of days ago that our Jewish son eloped with his Catholic fiance the day after he proposed...6 weeks ago!  They did it to speed up the adoption of her children,  However, they still want to have a religious wedding ceremony.  Neither is wearing a wedding band at this point.  I'm not sure how many members of her family know, but only two people in my extended family have been told.  In fact, it was only because my daughter-in-law wanted the parents to know that we were told.  They'd intended to keep it secret and get married as they'd planned.   
How does this affect the situation with a rabbi and priest performing a ceremony?  (From what I'd read, the rabbi would've done the actual marrying with the priest blessing the union.)  We had been married by a judge and then on our 25th anniversary had our rabbi perform a normal wedding ceremony, albeit without a ketubah. 

[Phx Mom]

Forgot to add...
Her kids would be Catholic.  The children they'd have together would be Jewish.
Does the fact they're legally wed act as less of a restriction on the rabbis who'd be willing to perform the ceremony?

[AJ]

depending on the state, the restrictions would include that the rabbi would not be able to officially pronounce them husband and wife since they are already married. And they would not sign a marriage license the day of the ceremony.  Their official anniversary would remain the day that they signed their marriage license