Mr. Yates was totally born in the wrong era. If were alive now he'd probably be on one of those reality shows that tries to cast someone in a Broadway musical. Mr. Yates only cares about the theater and it seems that the "great tragedy" of his life is the fact that his previous theatrical production at Lord Ravenshaw's house was canceled because someone's grandma had really bad timing when she died.
Mr. Yates and his theater obsession is of course crucial in getting the play going at Mansfield Park, which has lots of long-lasting consequences. The play brings characters together and also tears them apart. In the midst of all this, Mr. Yates stomps around rehearsing and then can't let it go when Sir Thomas crashes the party and puts the kibosh on the acting. Poor Mr. Yates will never win his Tony this way.
Mr. Yates doesn't just love the theater, though; he also has a very theatrical, dramatic personality. Take his reaction to Sir Thomas's return:
He had known many disagreeable fathers before [...] but never, in the whole course of his life, had he seen one of that class so unintelligibly moral, so infamously tyrannical, as Sir Thomas. He was not a man to be endured but for his children's sake, and he might be thankful to his fair daughter Julia that Mr. Yates did yet mean to stay a few days longer under his roof. (20.10)
Sir Thomas is made out to be Satan here, since Mr. Yates is clearly something of a drama queen. This passage also reveals Mr. Yates's other great love: Julia Bertram. He seems to genuinely care for her and though the two elope rather hastily (which perhaps has something to do with Yates's flair for the dramatic), we can infer that they most likely have an OK marriage.