It just goes to show you that you don't find magical bishops that everyone else somehow overlooked just hiding in a field like buried treasure. You listening, Fr. Pfeiffer?
There are only a handful of valid, trained traditional bishops in the entire world. They are all well known and accounted for. You could go on a journey to find other valid traditional bishops and spend decades and not find any additional gems that everyone overlooked. Every apparently traditional bishop that everyone seems to overlook is being overlooked for a reason. Validity questions, skeletons in the closet, and other problems. Every single time you "discover" a new traditional bishop, he will turn out to be a fraud con artist like Ambrose Moran, be married like Bishop Fulham, or have other equally serious baggage.

Yeah, with the grave need worldwide for traditional priests and bishops over the past 50 years, the idea that you are going to get lucky and discover a new perfectly good one is naive at best. And priests are made at ordination ceremonies, not discovered.  

There was (is?) a sedevacantist bishop (?) in the Indianapolis area who was/is apparently married....with children.

But he had the “true faith,” so people kept supporting him.

Well, unless this was something weird he did just as a civil thing ... for some unknown legal reason.

We need to reserve judgment unless we have all the facts.

Isn't that what some liberals on Fisheaters said a few years ago? It became public that the divorced owner and a divorced member of her forum got civilly married. Some said "oh, but we shouldn't assume they're sleeping together or living like married people." What about the scandal of two divorced people being civilly married to someone who is not their true spouse? That's scandalous enough.
A priest shouldn't be married to anyone. Civilly, inside or outside the True Church. Any level of marriage for a priest is an absolute scandal. That's what Martin Luther did, married a nun, remember? And this was in Florida. There is no obscure law or pragmatic reason why a priest would need to get married, on the books, technically, or otherwise.
Please suggest a law or circuмstance that would morally allow a priest in America to get married, even a sham or civil marriage, so I can verify if it might be true.

Any chance it’s a different Terrence Fulham than Bp. Fulham?

Is his wife still around?  What is / was her background?  If she was retired from the military than her husband would be entitled to free healthcare and her pension until he died.

I had an aunt who cared for a kind widower / WWII Veteran.  He said his deceased wife was his one and only true love.  He had no desire to ever be with another woman after she died.  My aunt ant he shared a house and all the bills. They had separate bedrooms and a strictly plutonic relationship.  Not too long before he passed away he married her so that she could continue to receive his military pension and health benefits .  She had cared for him for so long he wanted to make sure she was cared for before he died.

Maybe she was taking care of the Bishop?

I had an aunt who cared for a kind widower / WWII Veteran.  He said his deceased wife was his one and only true love.  He had no desire to ever be with another woman after she died.  My aunt ant he shared a house and all the bills. They had separate bedrooms and a strictly plutonic relationship.  Not too long before he passed away he married her so that she could continue to receive his military pension and health benefits .  She had cared for him for so long he wanted to make sure she was cared for before he died.

Maybe she was taking care of the Bishop?

There are many kinds of valid marriages, good bad and in-between, including the Josephite variety and marriages of convenience like you describe above. However, a priest may enter into no type of marriage. Not even to save a life. Not even to save a thousand lives. You can never commit mortal sin to achieve some good. It's basic moral theology. I shudder to think what kind of advice this priest gave in the confessional.