When your an animal what is home. I'd say with your loving friends taken inside when it rains and snows talked to and petted each and every day, loved and appricated... That sounds like home, to me.
It is where you find comfort and peace. I don't think it is different for a pet..If you have ever lived with one, you know they have personalities just like humans. Even when your home isn't exactly as it should be it is still your home. Loved or unloved it is home where what little security you have ever had is. Our pets feel this too..
Abandonment is not the answer, Find someone to help, you don't throw your kids out the door... Your pets are just like your children, they look to you for everything
Be a good parent to both your kids and your pets....Nelda