snip excellent advice from several people

Ahh...much more good advice, but it does bring up one more question. This
tree once sprawled with very long branches. The guy that had the property
before me butchered it back, and now it have these very thick 12" or so
branches that leave the main trunk and go about 15 feet or more, and stop
because he cut them all off. From these is a lot of new growth sprawling all
over. I should take som pics of inside the canopy so you can see what I'm
describing. Also, two main branches that are over 12" thick all but cross
each other. I could cut one off, but it's quite large and would leave a big
scar - again let me see if I can get some pics so this makes more sense. The
challenge here is that this is a big tree and the branches themselves as
they branch from the main trunk are over very thick. I think the main trunk
itself is easily 36" diameter. Hmm...tomorrow I'll measure it and take pics
and post links to them here so you can see what I'm describing. It's a big
beautiful tree, and I'm willing to invest some time and effort to save it.
It gives a lot of shade, and there is a rope swing on one of the branches
that my girls love (should this be removed so it doesn't damage the limb any
more then it has?).