Elves and Dwarves had a lot of ups and downs over the ages according to the lore, and some of it is intentionally murky. When they first met, the Elves hunted them like animals, but then they made up after they figured out it was a misunderstanding. There was some killing in the first age over jewels & a silmaril. They're also just completely alien in nature to each other, which in Tolkien's lore (and in common sense) meant that relations were difficult.
Since we can't pinpoint exactly when this series is supposed to be, or what was already changed in the lore, it's hard to say exactly where they should be at during this point. It's clearly right before the Doors of Durin were made by Celebrimbor and Narvi though, which means their relations should be on the upswing or at least about to pivot.
From the Fellowship:>Well, here we are at last!’ said Gandalf. ‘Here the Elvenway from Hollin ended. Holly was the token of the people of that land, and they planted it here to mark the end of their domain; for the West-door was made chiefly for their use in their traffic with the Lords of Moria. Those were happier days, when there was still close friendship at times between folk of different race, even between Dwarves and Elves.’ ‘It was not the fault of the Dwarves that the friendship waned,’ said Gimli. ‘I have not heard that it was the fault of the Elves,’ said Legolas. ‘I have heard both,’ said Gandalf; ‘and I will not give judgement now.