Why would you need this to happen in the SSPX chapel? Would you not want to get married in the parish that is your home parish, olr the parish that you will attend as a married couple?
If it is just a matter of finding a “pretty” location, perhaps ask about getting married at the cathedral?
If1ke is correct, and your fiance is still attending SSPX Masses and you two haven’t discussed her attending at the Catholic parish regularly, and bringing up your family at a parish in communion with your bishop and Rome, than you two have a lot to discuss, which should take a huge priority over the wedding planning.