I'd say you closely supervise the puppy/kid interaction. It could end up that your puppy will turn into a vicious dog that you will have to put down. It really wouldn't be fair. Although I suppose that would be a natural consequence. I think that is how you pick the battle. If the natural consequence is so negative that you don't want to deal with it, then that is the battle you fight.

My husband sounds like your husband. He's a lot more picky about the little things, whereas I tend to let these things slide. I don't nit-pick about eating. I believe kids will eat when they're hungry. However, I do enforce no snacks between meals if they don't eat their meals. The couch thing, I wld let slide. That's what couches are for, relaxing. As for the puppy, I wld be very firm about how an animal is handled. They may just be playing now, but if you don't nip this in the bud right away, your child cld get very hurt later on. In situations where harm can result, I wld absolutely step in and do whatever I need to to fix it. I wldn't just sit back and hope nothing bad happens.
One expl of a battle I picked was over my son brushing his teeth. My son is a very independent minded kid, and he wants to do everything himself. While I knew brushing his teeth for 10 secs wasn't going to get the job done well, I also knew he was exhausted. For me, it wasn't worth fighting w/ him over brushing his teeth better, especially since he was so tired. I told him that b/c he was so tired I wldn't push the issue, but in the morning he needed to do a better job.