Branch falling off old apple tree

A large branch just fell off an old apple tree, about 20' tall. next to the house. Also in our orchard, a branch fell off a small pear tree that was loaded with pears. I think the likely causes of both were the weight of fruit and stressed because of drought. Not sure what the best course of action would be:

I can just dispose of the apple branch and leave the rest of the tree but the tree leans quite heavily one way and with this branch gone, most of the weight is now on the side the tree is leaning.

Another option would be to remove the tree completely. It was a well established tree when we moved here 40+ years ago and has had mushrooms growing on it all the time, a variety called turkey tail I was told which feeds on dead wood so not likely to harm any living material in the tree. The tree is likely over 150 years old as the old couple who lived here before us, the lady was over 90 and said the tree was here when she was born in the house so at least 130 years. At an apple fair at Reaseheath, the local agricultural College, I was told that it is a Gravenstein. I don't really want to cut it down.

If I leave it up, I was wondering how much I could trim the rest of the tree, to take some of the weight off it, without causing too much harm? It always has far more apples than we can use but is delicious, particularly as stuffed and baked apples.

          

The pear tree is a lot younger. I planted it about 10 years ago. The way it has broken has badly damaged to main stem. There is a weaker stem you can just see on the right in the second picture below. Any suggestions what you would do with this?

               

Its always sad when apple trees shed branches. Our old apple trees were planted for the War Effort apparently, so nowhere near as old as yours. They used to lean over regularly and we would brace them with a notched length of timber - to make a sort of tripod. Some of the heavily laden branches here are supported in the same way - its the only way I can walk beneath them!
Hope you can find a way to save yours.

I'm no tree expert by any means, but it would be a shame to lose either tree. Perhaps a tidy up of the wounds, paint with something, then fashion a prop of some sort. Not much else you could do if you want to save them.