Q.tiny roots
How can I get rid of tiny roots that continually invade a flower bed? I can even pull them out in clumps. Flowers won’t grow hardy. {please don’t suggest cutting down nearby trees]

Consider burying barriers around the beds to help keep the roots out. If you are sure that the roots are from the trees, it may be that the trees find something in the beds that they need and this is making them aggressive in their root growth. You may want to have the soil closer to the trees tested so that you can determine if there is anything the trees are lacking that you can add. They may also be seeking water. Make sure that the trees are getting enough water as well.