I really want to go and cut my neighbor's tree so that it is in line with my fence.
Why do you want to cut your neighbor's tree in this way?
I would prefer for their trees to not throw shade onto my garden.
It's fine to cut your neighbors tree in the way you choose, as long as you have permission from them first. If not, they'll be upset that you touched their property. They may go to their HOA over your actions and possibly have you punished.
I don't care about what HOA say, I have to do what I feel is right.
Well if you do not get their permission first you may just create a larger problem then just having shade on your garden. If you ask nicely they may actually appreciate you cutting the trees. If you do it without asking they may view it as being disrespectful.