Have to agree with rockm, little rats are always digging around my yard or pots. Last year had a peanut plant pop up in one of my tree pots. They like to burry food. I have what I think is an aluminum screen used for plaster jobs, it has diamond shaped punch outs, but the edges are all kind of sharp, so I don;t think they like pawing around a pot that this stuff covers.
Getting rid of the trees or the squirrells are the other options. Some mouse traps placed around your trees may give them enough grief to play elsewhere, a dog or a couple of cats can help too. Then there is always firearms