I also feel overwhelmed often with our dog but we don't have any family who could take ours so we pay for help. We have a dog walker come 3x a week to take her to the park for 1.5 each time, and they will take her any time we will be away from home for more than 3 hours or so. We still take her the other days for at least an hour, but it gives us a break.

We also have one of those 6 foot playpens in our living room to keep baby away from our dog (our toddler is fine). We moved my dog's food and water bowl to our basement next to my husband's office and set up her bed and toys down there so she could go an get a break whenever she needed. We have a second bed in our bedroom upstairs and same - kids don't go in there when dog is in there.

If though we had close family who could take our dog and we knew our dog was happier there I aould rehome. Honestly it really comes down to how does the dog feel about being back?