Picking up the rocks and covering the roots in your yard might be the logical solution. Or one of these.

Here is a link that might be useful: rough terrain mower

"wayne440" is on the right trail about the rocks and roots. Your terrain is "telling" you that it will destroy your lawnmowing efforts and machine unless you change something. Even the rough terrain mower in the link (which is a good one) is not going to cut through the hard stuff.

So it's not really a question of which mower, but rather modifying your terrain to be able to mow it.

Best Wishes--Carl

I cannot cut down the trees since they belong to my next door neighbor and they run into my yard. How do I go about covering them?

You may could cut the roots at the property line and pull them up? Or just put soil over them and plant grass?

I was thinking you could create a border on your side of the trees, mulching the ground from there up to the trees, and not having to mow that area any longer. You could also try a low groundcover in the same area. (As to cutting the roots, that risks damaging a tree enough to have it die and possibly fall onto your property). Best Wishes--Carl