Not agreeing on how to train a dog can cause many problems in a relationship, trust me, I know. My Lacey is the type of dog that needed total consistency as a puppy and hubby didn't go along much with it. While she has turned out to be a great dog, there are times when hubby is around she will disobey me because he is there. Our Mandy, who we recently lost, was an easy going dog, so not many problems there and I'm praying Layla will be also.
I too am the primary caretaker of all four of our furkids but hubby helps any time he is needed. Both Lacey and Mandy had many surguries/illnesses so of course we both had to pitch in. And now with a puppy of course we both need to take care of her.
If your boyfriend is not interested in your two dogs you are possibly headed for trouble with your dogs and your relationship. I wish you good luck with this situation.