I can see the logic - the same root stock and a branch of the variety of the same tree. I'm no expert but I don't think the branch will be the problem (providing it is healthy) but the rootstock that has sent a sucker is perhaps not a good idea. Suckers tend to be reversion to wild type (not always) and may not grow true to the original root stock. If it was my tree, I'd be removing the sucker.
If you want to keep the apple variety line going for sentimental reasons, perhaps you could buy fresh root stock from a supplier (tree nursery) and try grafting on to them, or maybe some aggressive remedial work on the original tree (you might need to get a tree specialist) to try and rescue it?