From a priest reader:
I have become acquainted with a family in my parish (Diocesan sponsored EF twice a week) and the parents were married in a SSPX chapel. My question to you, after having posed this to three solid, traditionally minded priests, is this: What is the canonical status of that marriage? Is the marriage considered valid but illict? Is it similar to a protestant marriage that needs to be canonically regularized within Holy Mother Church? Or, is it considered invalid because those in SSPX are under different canonical standards than a non-Catholic? Or, is it simply valid, end of story?
Perhaps you have already addressed this issue and can direct me to a answer. Either way, your insight would be much appreciated.
I have addressed this before, but repetita iuvant, as they say.
The marriage would be (most likely) invalid not because of a lack of form, but rather a defect of form.
Even though canonical form was followed, there was a defect affecting validity because the priest who officiated lacked delegation (c. 1111) from the parish priest or local ordinary.
Moreover, the priest (if he was a priest of the SSPX) is suspended a divinis. He therefore cannot be delegated to officiate at a wedding (cc. 1109 and 1333).
Some argue that c. 144 (on common error and probable doubt) applies. This argument is without merit, since it does not cover willful ignorance.
The couple in question should seek a sanatio in radice (retroactive convalidation). They can apply for this through the diocesan tribunal.