My dog ate a carpenter bee and has been lethargic and stumbling ever since 2 full days now.  I thought at first he had strained a foot, because he was holding one up, but the next day he was holding the other foot up and both back feet seem to hurt him now.  The bee might not be related?  Do they have toxins?

I have never heard of any bee being poisonous on ingestion and I can't find any information to suggest they could  be. Female carpenter bees can sting which could cause swelling in the
mouth/throat and potentially breathing difficulty if the swelling is
severe but this would likely be an acute problem you would have noticed
at the time.

So I would say that if your dog is unwell (and you are the best person to judge) it is probably not related to the bee at all. Of course if you think there's a problem then asking your vet is the proper action.