Could you hire someone to come in and walk them during the day? Give the boxer the schedule it needs without you having to worry about it? If the dog is otherwise a good dog, that might be just what he/she needs. You can ask the vet if they know any reliable dog walkers or dog sitters that you could trust.
The little dog....what about explaining to the child that IF you keep the dog, she needs to do x and y to help. You say that your DH has tried to train it. Have you hired anyone to evaluate the situation to see if there's more? Is the dog stubborn or have other issues, like medical problems? You're going to need baby gates anyway, so what about gating the dog to certain areas?
And what does your DH say? How does he feel?
If you still rehome them, consider fostering them for a breed rescue, so that they'll help with the placement but the dogs aren't taking up more of the rescue's space.
ETA: try not to make it all about the baby. If you do, the older child may resent the baby for making the dogs leave. Stick to other current facts if they have to leave and also decide if they both have to go or just one. I would not try to replace them with another pet, because even small critters need their care - cage cleaning, vet care, food...which all falls to you as the adult.