Tibetan cherry... 2nd try.....

You can trim them back but they will re-grow. Is the tree on the left in your garden on in the field?

 

Cut off the overhanging branch of the tree on the right, move your new tree left a little and a little more into your own garden and it will be simply breathtaking in a few years time .... and tell hubby not to be so negative LOL

 

P.S. when you are cutting off the branch, cut with a clean saw up to but not into the little knuckle you will see next to the trunk ... it is that little knuckle that grows over and protects the cut

 

Yes it is my tree and thanks for the advice.... Planting the weekend hurrah!