Sorry, I saw that your dog is female...
I had a really hard puppy a while back. Pooping and peeling inside can be stopped with treats and consistency. You might have to set an alarm and be extra aware of when your pup drinks water. You should take them out first thing in the morning and supervise, tell him 'go pee'. Immediately after he finishes peeing offer a treat and tell him 'good dog' then tell him 'go poop' if he doesn't within 3 minutes, say 'too bad' and go inside. Then try again in two hours. Take him out every two hours and he should get it after a week. If he goes in the house, tell him 'too bad' and immediately put him in the kennel for 30 minutes (make sure you time it) then take him straight outside and do the treat thing again. He should also go out right after he drinks water, and right after he eats. Be consistent and you will start to see improvements. It is hard to stay on top of, I'm not saying it's easy. If it seems like it's too much, finding him a new home might be the best. Just make sure others know he is not house broken or he'll just end up in a shelter because someone else isn't as likely to want to put time into finding him a good home. Good luck. Also, having tons of chew toys around helps. If he starts to chew on something he shouldn't, give him a toy that he can chew on and say 'switch' this worked for my problem pup after just a few times.
I would tell your boyfriend that if he wants to keep the dog, then he has to clean up 100% of the pee and poop. It's dangerous for you to be exposed to fecal matter. You'll have to work really hard with her about chewing, maybe give her tons of chew toys, and take her to obedience training.
If after a few months he isn't keeping up with his end of the deal, then you get rid of the puppy. Once you have twins you will be so tired and overwhelmed that you won't be able to do anything else. I hope that he will help you out with feedings during the night, because otherwise you'll be so tired.
I'd definitely ask him to take care of the dog for now. good luck.
Unfortunately, I can't tell you what to do....you guys have to do what you feel is best for your situation.
Good luck and Congratulations! :)