E.P.
No judgment here. Sounds like you are really struggling with this. Congratulations on the new baby. Sounds like you truly have your hands full!
Hinsdale Humane Society will do their best to find a good home for your pet and will not euthanize the dog if they don't. They are good people. It's a good back-up plan if you are still trying to find a new home for your pet and you are unsuccessful.
http://www.animalshelter.org/shelters/Hinsdale_Humane_Soc...
Best of luck to you.