To cut the tree or Not to cut the tree

It's spring again, the grass is green, the flowers are blooming, the leaves are out.... and the caterpillars are back. It's awful!!! Last year the apple tree in the back had about 6 caterpillar tents. This year there is about 12. They are really a nuisance.

 First the tents start growing, then you start seeing the"eggs" or larvae, after they start coming out the tent and down your tree. I swear there's tens of thousands of them all over your backyard by the time it's done. They get in everything, it's like an invasion. After that they cocoon on all your stuff (barbecue,lawn mowers, bikes etc..). Then they become moths and some of them manage to enter the house. This hole process lasts about a month. The kids are terrified and won't go out there for that period.

 This year there are more tents. I was told that the tree was sick and that I should be getting rid of it. I like to think of myself as someone "green", I recycle and do compost etc.. so it's hard for me to get rid of a tree.(My neighbor cut down his perfectly healthy tree last month and I really let him know how stupid  I thought that was. He said it was leaning on his ugly old shed).

So what do I do, my uncle's coming next week and he offered me to cut it. Kill the tree or keep the caterpillars???