Dear W =
I'll keep this simple: Keep your dogs.
Kids grow up eventually and if this mom thinks she'll be able to shield her son from dogs for the rest of his life, she's a bit deluded. Doesn't it make more sense for you, her and him to sort of, I don't know, tackle this fear early and nip it in the bud? ...I'm of course talking about approaching this in a thoughtful and sensitive manner, not locking the kid in a room with four pit bulls... maybe even seeking professional help to help the kid get over his fear. I'm no expert on kids, but I don't think they simply 'outgrow' these sorts of issues completely on their own. In fact, I think this sort of fear might be likely be beget other fears. Once the kid realizes (consciously or not) that if he says he's afraid of something him mom will bend and twist the world to make him more at ease... well, that could set in motion one big ball of unintended consequences.
But you've got to approach the mom with sensitivity too. You can't puff out your chest and say "screw your kid, I'm keeping my dogs." ...but you have to let her know that your dogs are, in their doggish way, members of your family... Getting rid of them will lessen your quality of life and definitely cause the dogs a lot of trauma (some studies suggest that dogs, once bonded with their original owners, never fully get over being separated from them.) So when you talk to her about this, preferably without the dogs at your feet and her son in her lap... Let her know you're willing to explore any options that would keep you together as a couple AND let you keep your dogs. If she is completely unwilling to hear that and move forward then you might want to re-evaluate your relationship. IS she using the dog issue as an excuse to break up with you? ...and conversely, are you sticking to your guns because you love your dogs? ...or because this might just be an honorable way out of the relationship?
You have to be honest with her, and honest with yourself. Dogs and kids have a few things in common, they can sense fear, and bullshit. Don't be a disappointment to any of them.