Hey Josh, under your circumstances you need to be careful...
Before ever attempting to mix any angels... or fish for that matter... you need to make sure the new fish is 100% healhty, fat, and adapted to captive life... even when done right, pairing is stressful on the fish (or in our cases... think of when you met your wife or significant other)... So, making sure the new addition is fully quarantined, adapted, and disease free is an absolute prerequisite... and should be even when not attempting to pair...
So, with that said... we'll go as is we're assuming the new little girl is in that state... IDEALLY you should remove the larger individual that is established for at least two weeks or so and place the smaller individual in your system for those two weeks to settle. That is not necessary however, but again ideal. For those experienced with this you could transition the new fish in by other means... I am actually going to start a separate thread on this principle because it is so important yet so overlooked and I get asked questions so many times about this. Allowing the two fish to see eachother but not tough is the other route... adding the new fish in either perhaps a sectioned off part of the tank with eggcrate, or in a small plastic "critter keeper". ALWAYS be sure the new individual is kept in an environment that is as stress free as possible... prolonged STRESS equals onset of disease and death many times... so always make sure your fish is calm and relaxed with a place to seek refuge... Obviously when moving the fish they are stressed but this short term stress is not an issue most of the time... After a couple weeks of seeing eachother the aggression is usually tolerable for the new fish and it works out... but again be aware there are many dynamics to this... leaving the tank light off for a few days also after mixing is a tactic that lessens aggression also... it's a cloudy day on the reef and your corals will be fine... ambient room light will suffice for the fish...
So, you could attempt using those means, but it is important you have experience handling fish to do this... those are the basics but again you could really write a book on all of the nuances and tricks...
The reward however is fantastic! Seeing your angels interact and spawn is such a treat each night...
Copps