Deciding as a couple to be a "package deal" (new partners gotta be with both of us or neither of us) so rarely goes well. Like, really, it's just the most counter productive way to try to avoid jealousy.
As for the fluid bonding thing, I assume you had a condom on but your partner didn't have a glove on. So if their rule was "no penetration without a latex barrier" it makes perfect sense that fingering would have been off the menu.
Apologize sincerely and tell the new girl you've gotta take a break, possibly a permanent one, while you two work things out. Then settle in to try to do just that with your partner. Frankly her behavior comes off as pretty selfish/self-interested, but I imagine it's probably a matter of lack if experience and her truly not knowing what would work and what wouldn't and how she'd feel. There are some great resources on www.morethantwo.com
. All you can do is talk, give her time the way she gave you time, and see where things go. If you two do decide to re-open up at some point, you can try not to make the same mistakes.