They began in 1999 they say as a missionary society but did not become a Domincan Third Order until 2005.
With the group becoming Dominican, and being from New England, did they hook up with Bp. Robert McKenna from Monroe, Connecticut? While he was ill a couple years ago he had a a priest assisting him at the chapel who did celebrate Mass also in Massachusetts.
Bp. McKenna is not sedevacantist but rather sede-impeditist.
I couldn't find anything on how they claim Apostolic succession.
I am familiar with McKenna, he's the SSPV guy right? And the Priest you're talking about is Brian McMahon the convicted killer right? (only accused of forcing an abortion).
Is Sed-Impeditist, the belief that there is a Heretic occupying the Papacy or the one where the belief is that the Pope is a hostage of the College of Cardinals.
Either way I think this group feels that the Popes since Pius XII have not ascended to the chair of Peter because they are Heretics, though they don't seem to have commented on Benedict yet.