Mr. Osborne strongly encourages his daughters to be friends with Miss Swartz. He brags about how colorblind and inclusive he is, but obviously it's just because of her money.
Mr. Osborne is also really hoping for George to marry her. He checks out the way her money is invested and does a little digging on the Stock Exchange. All seems good there. Fred Bullock, a banker on the Stock Exchange who is engaged to Maria Osborne, tells Mr. Osborne that they better snatch Miss Swartz up pretty quick before a member of the aristocracy comes and steals her out from under them. (An aristocrat would have a title, and thus be higher up socially than the Osbornes.)
Mr. Osborne offers Miss Swartz's governess five thousand pounds to seal the deal between her and George. He also orders George to marry Miss Swartz. George kind of hems and haws and says that he'll wait until after the military campaign is over.
His father isn't having it. He orders George to come to have dinner with the family and Miss Swartz every day and woo her.
Miss Swartz isn't in on all these schemes going on behind her back. But George is hot, and she is starting to be into him.
The next day, George comes home for dinner after hanging out with Amelia. He is shocked at how even more gross Miss Swartz seems after Amelia's delicate and feminine qualities.
Miss Swartz sees Amelia's name on the title page of a book and realizes that the Osbornes know her school friend.
George is psyched to talk about her, but his sisters freak out because no one is supposed to mention the Sedleys anymore in the Osborne house.
After dinner, it's clear that George and Mr. Osborne have to get into it.
George is all haughty and obnoxious, telling his father that he is a much better gentleman and is farther removed from the business end of where the family money comes from. This is a sore point with Mr. Osborne, who is totally enraged.
Mr. Osborne makes an ultimatum – marry Miss Swartz or else be totally cut off.
George says Miss Swartz is the wrong color for him and storms off.
George then finds Dobbin, tells him what has happened, and says he will marry Amelia the next day come hell or high water.