I want to give away my children's pups
Why are you wanting to get rid of them?
I've had the pups for years, but recently I'm finding them so annoying.
It would most likely break your children's hearts to give away their pups. Instead of giving them away it may be worth talking to your kids and having them take more responsibility of the pups.
I like kids but I don't like the pups so I'm giving them away.
Did you hear me? You should see if there is some way for the kids to take more responsibility for the pups so that you are not as annoyed by them. They are you children's responsibility, so you should not take them away from the kids.