To the OP: from personal experience, I will say that the SSPX priests have no interest in getting with the local bishop to get permission to witness a marriage. They were supposed to do that when my husband and so got married in the SSPX chapel we attended, but we literally got told “we aren’t even going to try” to get permission from the local Ordinary. Consequently, when we left the SSPX several years ago, and began attending our FSSP parish, we had to get with our pastor and get a Radical Sanation done through the Local Ordinary’s office… previous to which, WE WERENT ACTUALLY MARRIED!!!
Yes, it was a shock to us, but according to the Catholic Church, we weren’t married because the SSPX priest didn’t have permission.
Don’t let your child “get married” by an SSPX priest!! That’s my recommendation, anywho.