Other than the fact that Bilbo chooses Frodo to be his heir, are there more long standing reasons for the feud between Bilbo and the Sackville-Bagginses?
Their feud dates from Bilbo's return from his adventures in the Hobbit:
Bilbo's cousins the Sackville-Bagginses were, in fact, busy measuring his rooms to see if their own furniture would fit. In short Bilbo was "Presumed Dead," and not everybody that said so was sorry to find the presumption wrong.
Many of his silver spoons mysteriously disappeared and were never accounted for. Personally he suspected the Sackville-Bagginses. On their side they never admitted that the returned Baggins was genuine, and they were not on friendly terms with Bilbo ever after. They really had wanted to live in his nice hobbit-hole so very much.
Bilbo thinks they stole from him; the Sackville-Bagginses feel like that Bag End was stolen out from under their noses from his reappearance (and then a second time by Frodo being made heir):
'Ours at last!' said Lobelia, as she stepped inside. It was not polite; nor strictly true, for the sale of Bag End did not take effect until midnight. But Lobelia can perhaps be forgiven: she had been obliged to wait about seventy-seven years longer for Bag End than she once hoped. (The Fellowship of the Ring)