Can you adjust your wheel so it is not pulling the yarn in as hard/fast? Too much twist in the thinner spots will also make your yarn more likely to break as all of the twist gathers there rather than in the slightly thicker spots.
Try really drafting out your fiber so all you have to do is add a bit of twist to it, and aim to just get it on the wheel for the time being- you can go back through the bobbin with additional treadling after it is full if need be to add more twist later. My guess is that when you are rejoining you are treadling? Instead, allow the twist from the single on the wheel to travel to the one you are trying to join- you may have to pull a bit off the bobbin in order to have enough twist if the area leading up didn't have much twist to it.