Your dogs will be a bigger problem than your partner. The Fair Housing Act, which is the federal law governing housing discrimination, specifically includes seven protected classes: race, religion, color, national origin, sex, disability, and familial status. You cannot be singled out for familial status. Dogs, however, are not a protected class.
Dogs often chew the door frames and ruin carpets. Even worse, if your dogs appear on one of the many "Dangerous Dog Breeds" lists (check Google), your landlord may have no insurance protection in the event your dog bites someone. The person who got bitten will sue you AND your landlord. Your landlord's insurance company will say that, since the dog appears on one of those lists, and your landlord ignored it and rented to you anyway, that's negligence. They don't cover negligence. So, smart landlords don't rent to people with dangerous dogs. Here's a link to the longest list I have found to date: http://www.dogpolitics.com/my_weblog/2007/05/list_of_banned_.html
So, get rid of the dogs and keep your roommate.
The hard part will be finding someone who will rent to someone with 2 dogs. Be prepared to pay a larger deposit because of them.