Could their dogs eventually end their relationship?

Could their dogs eventually end their relationship?

"I've been with my boyfriend for 3 months and I'm worried about our dogs. They're both used to being the only dog in the house, and when we've tried introducing them they've hated each other. Neither of us would ever give up our dog, so I'm worried about what'll happen when we eventually move in together. Could this end our relationship, and what would you do in our situation?"