Well, why don't you keep the dog and rehome your DS instead?! no?! 
I agree that it doesn't sound like you're trying very hard. All my DC are currently at school, but I still manage to walk all four of my dogs twice a day, and that usually involves 4-6 seperate walks as one is a puppy that needs training and another is doing recall work, so seperate walks for now too. The housework does suffer but so what?! It will wait.
I agree it makes more sense to drive to the baby clubs and walk thw dog before and after you go. Two 30 minute walks with training included are better than one long 60 minute jaunt where the dog does as it pleases and runs about, especially for a dog like a Beagle. Also, you say you want to stay for coffee after the baby groups, it's not complusory. Personally, I'd choose walking my dogs anyday over boring old baby chat, or in fact, any chat.
Your dog hasn't chewed things because she's 'got the hump', she is bored and under stimulated. You also need to stop thinking of her like a child, she doesn't need your constant attention (although if you give it on demand, she'll keep demanding it) she needs exercise and stimulation.
Having a dog is having a different lifestyle, the dog must be a priority and it doesn't sound like that is the way it is for you. If you aren't commited to the dog then the responsible thing is to return to the breeder, but please don't make out you had no choice, you are making that choice.