Trees That Bleed Red Sap

Question

I have 4 trees in my garden that I think were set by birds. They are fairly smart trees, so I let them grow. In the Autumn they turn a pretty orange red before the leaves fall off, as they are doing at the moment. The trunks are a silvery grey. The leaves are similar to an apple leaf in appearance, but lighter green. One actually had a small white blossom on this summer then turned into a small woody brown berry. But in 2009, I had to partly cut one down, and it bled dark red sap profusely, and no branches have grown from it since–although sucker-like branches have grown from beneath the soil from the tree. They are very pretty foliage trees, and so far they are about 4 ft. tall and still growing.

Answer 1

It might be a Soymida Febrifuga. But that is not native to your area, but your desctiption of it is dead on this tree. Here is more information:
http://idtools.org/id/dried_botanical/factsheet.php?name=Soymida%20febrifuga