] I thought I detected a hesitation on Eleanor's part about inviting Catherine to Northanger - not because she did not want her company, but because she had some reservations about her father's motives in wanting her there.

In general, the General seems harmless to me. But a truly unpleasant thought did cross my mind, that fits with the uneasiness you describe. What if the General is thinking of Catherine as a wife for himself?

When he gave Catherine the tour of the house, and showed her the guest rooms, it seemed pretty clear that he was hinting that he hoped her family would soon stay there - as they might if there were a wedding between the two families, for example. But he doesn't really seem to be talking up Henry as you might expect he would if that were the match he had in mind. He seems to be talking up himself more. (although, as head of the family, it could amount to the same thing in his mind)