I agree with Tulip (and others) who have suggested re-homing the puppy. You saved his life and brought him back to health, but could not have known at the time that your life was going to change drastically. Please don't feel guilty about that.

It's a difficult decision, but your long workdays and his behavior with your cats makes this a stressful situation for all. You will need your time and energy to focus on caring for your mom. With the excellent care he's received so far from you he will blossom in another home, and the rescue will do their best to match him with the right folks.