"I do feel terrible to even be considering getting her re-homed"
Good. So you should. Because you would be terrible. She isn't even your dog to rehome!
I speak as a dog rescuer so I'm a little biased. I come across people who dump their dog when they have a baby with alarming and heartwrenching regularity. I pick up the pieces, I find the rescue places, I comfort the dogs, I pay for or fundraise for their dogs to be neutered, vaccinated, chipped, fed and housed.
And all the while I know that there will be a pound dog who could have taken that rescue place but who has been killed in the pound because some heartless fucker had taken the rescue space for their discarded family pet.
And don't get me started on the irresponsible people who bleat that they would rehome privately or sell the dog through the free ads....
On a more positive note I also speak as one with other experience. From the moment my DC came home from the maternity hospital they have lived with at least 2 large breed dogs. We currently have 3 big dogs, including, for the past 8 years, a rescued Lab. My kids have lived with god knows how many foster dogs and all manner of strays which I've taken in.
Those kids are 14 and 16 now. They are both rescue volunteers, they are both dog-savvy and animal lovers. Neither has been bitten in their lives, neither has been in the least bit ill as a result of a bit of dog hair, slobber or mud. I have a Dyson, simple solution to dog fur!
Sensible measures - don't leave DC and dog unattended, don't let DC climb all over Rover or pull his tail, don't neglect Rover and consign him to the kitchen when DC come along... I'm sure others can suggest more. There will be the odd ones on here who suggest you get rid of your partner's dog - to them I say you're talking rubbish.
Besides all this... if this is the dog who your partner's children have been raised with, what's the stress? Dog knows what children are all about and I take it that DPs kids aren't suffering from rabies or missing limbs as a result of being raised with the dog?
:o