Sir Thomas Bertram is like a Dementor, from Harry Potter. OK, so he doesn't suck out people's souls. Though his daughters might argue that is so. No, Sir Thomas is like a Dementor of fun. He can suck the life out of a party faster than you can say "alohamora."
Sir Thomas is definitely not a fun, laidback, understanding, or even very affectionate parent. He spends a lot of his time scolding his kids and his niece Fanny. And he's also dangerously, and willfully, blind to his kids' faults at times.
After returning from his long trip abroad, Sir Thomas "meant to try to lose the disagreeable impression, and forget how much he had been forgotten himself as soon as he could [...] he was more willing to believe that [his children] felt their error, than to run the risk of investigation" (20.2).
In many ways, Sir Thomas functions as an antagonistic figure in the text. After all, his niece's fear of him causes her great distress, and his daughters' dislike of him drives them away from home in a fit of rebellious independence that ends up in some questionable marriage decisions.
But Sir Thomas is also a sympathetic figure. By the end, he's a failed parent who's acutely aware of his failure, which is a very painful realization. He understands that he's been blind to his own children. But he gets a second chance to be a decent father to the Price kids, who in many respects replace his own children in terms of his attention and his affection by the end of the novel.