It sounds like your mother had a soft, messy tree growing too close to her property line. It may have grown from a seed dropped by a bird, and it probably should have been yanked out of the ground as a sprout.

If you want to have a rowan, with its soft fruit to the birds, then it needs to be planted where it will not drop fruit or branches on a person, path, car or building. This means not close to a neighbor. And consider too, what kind of birds it will attract. Thrushes and waxwings are one thing. A hundred squawking starlings are another.

In my neighborhood people sometimes let mulberry trees grow big. They too, are supposed to feed the birds. Mostly they produce purple sidewalks and lots of flies. They too, should have been pulled out as sprouts.   

The internet says that rowans interbreed freely with other members of the rose family. Volunteer plants will be variable. So if you want a good one, go a nursery and buy a good variety with a predictable shape and size, pretty flowers and lots of color.

If your mother's place were mine, I would hire somebody to remove the rest of the existing rowan tree and take away the debris. If that can't be done, stack the wood up neatly and let it compost away. And if she really loves a rowan, buy her a good one and plant it in a good spot.

I'd probably give up on the Christmas and birthday presents, too.