We often get dogs with broken nails at work. Cut the nail where it is broken and apply quick-stop and lots of pressure. The bleeding isn't serious, with the quick-stop and pressure it will stop. For now, leaving the nail like that, the broken piece is moving and irritating the quick. It's best to just cut it off and get it over with. I'd have someone distract her with tons of treats and loving so that she doesn't even know you're cutting her nail. Most dogs won't carry a grudge though -- I am the worst for quicking dogs, I always try to get the nail as short as possible (on dogs with really long nails) and I often groom the same dogs, and none of them are difficult for nails if they weren't in the first place. It's true that some bleed more than others, but it's nothing that some quick-stop and pressure won't stop.