Re: does the tree need to come down?
Tree of heaven so-called is the Ailanthus, a chinese import that grows very rapidly and seeds itself freely and is IMO an invasive species. As fast-growing as they are, they reach old age very quickly too. The wood is extremely light and pulpy, so the danger of it falling apart as it rots from within is real. I would get rid of it and grind out the stump or spray with the most potent brush-killer you can find. New shoots will come up from the roots, and the seeds will sprout when the sunlight hits them. You will probably have a million seedlings next year.
Remove not the ancient landmark, which your fathers have set.