First of all, congrats on your pregnancy!
With my daughter, we used a little cradle (like a bassinet) that sat right beside the bed. It felt like the safest option to me. With a bassinet or cradle, they are up off the ground at about the level of your bed, so they still feel nice and close but still completely away from the dangers of cosleeping in the bed with you (accidentally getting covered up with blankets or pillows, etc). It's the perfect solution for when you're up every 2 hours feeding, too.
Especially if you breastfeed, you never have to leave your bed that way. They are next to you, but still in a separate bed that isn't attached to yours. One reason I didn't trust my daughter with the cosleepers that attach to the bed or sleeping in bed with us is that she moved around sooo much, even as a newborn. She would have buried herself in blankets in minutes. In the cradle, I never had to worry about any of that, but she was still within arm's reach.
I don't really have tips for retraining the dog, but maybe you can find a happy medium by keeping both of them near you at night. If you use a cradle or bassinet for the baby, your dog could probably keep his spot on the bed. Good luck, and congrats again on the pregnancy!