Here's the thing...You haven't yet tried separating them into their own cages, correct? That would be step #1 before I ever thought about re-homing her, because #1 it's extremely likely that once she's separated into her own cage or "territory" and the stress of having to share her territory with another bird who she obviously isn't very fond of, or at least not in the way you wanted her to be, that she'll settle right down for you, and you'll then be able to work with her one-on-one every day and actually form a bond with her, rather than trying to form a bond with her while she's experiencing the stress that she is while sharing the same territory with the male...And then #2 is the fact that if you re-home her, she's likely going to go through some serious mental/emotional issues from being totally separated from you, from the other bird, and taken from the only environment she's ever known, even if she's not seemingly bonded to anyone right now (she is, trust me), and whomever adopts her is going to have the same problems with her and will re-home her, and again, and again, and again...As someone who has worked for a large Avian Rescue for over 8 years now, I can tell you with authority that you'll only be sending your bird into an endless cycle of re-homing...Not something you should do until you at least try separating them...
***The thing of it is that whenever you put two birds together, even if you do it when they are both babies, even if they are siblings, there is absolutely no guarantee of what type of relationship or bond they are going to have. And just like relationships between people are very complicated and have many different possible dynamics, so is the same with birds. You said that you "Only got two birds because you wanted them to have each other as friends", and this is an extremely common mistake that many, many people make every day when bringing birds into their homes and their families. And Love Birds are no different than any other parrot species, in-fact they actually seem to be more extreem when it comes to them accepting another bird as a "friend" or partner, it often just doesn't work out.
The idea when you bring home any single parrot, regardless of the species, is that they are in-fact Flock-Animals, and they do need to bond closely with someone, but that someone is supposed to be you or someone else in your home. No other birdy "friend" is necessary at all, nor is it often wanted. And the fact of the matter is that the rule of "Never buy a second bird as a friend for your first bird, but only bring home a second bird as another friend for yourself" is and remains forever true. And the reason is because you cannot EVER have any idea how two birds are going to get along...So the answer to your question above is a resounding YES, you may get the exact same result if you bring home any other bird in the future, it may or may not get along with your current male Love Bird, and then there are also many different types of relationships/bonds within whether they simply like each other/get along or not. So once again, unless YOU WANT ANOTHER BIRD AS ANOTHER COMPANION FOR YOURSELF, DO NOT BRING HOME ANY OTHER BIRDS AS A "FRIEND" OR COMPANION FOR YOUR EITHER OF YOUR CURRENT BIRDS, BECAUSE IT'S LIKELY TO NOT WORK AND END THE SAME WAY...The idea should be that you and others in your home are your bird's companions/friends, they bond with you, and you and the others who live in your home are their "Flock"...
***As far as your female Love Bird goes, I would highly advise you against re-homing her until you separate her from the male and into her very own cage with her own toys, perches, food and water, etc. (though I would leave their cages in the same room and close enough together so they can still see each other and talk to each other)...That in and of itself might very well result quickly in a change in the female's behavior and attitude, because she no long has to feel like she's constantly "defending her territory' from the male Love Bird...And then the idea would be that you start spending one-on-one time with her every day, working with her and bonding with her once she's no longer living in the same territory as the male...What you will most likely see happen over a short amount of time if you do this is that not only will the female's attitude and behavior do a complete 180, but BOTH BIRDS will form much stronger bonds WITH YOU, as you will become both of their companions. And they can still spend supervised time out of their cages with each other, typically once two birds in this situation are separated into their own territories they also start getting along with each other much better as well. It's all about jealousy, territoriality, and being forced to live with another bird and share territory with another bird that they just don't have the type of bond with where they want to do that.
I'd say that if I had to catagorize the type of relationship that your two Love Birds have, they have a "We simply tolerate each other because we have to, we don't hate each other or even dislike each other, but we also don't love each other, and we certainly don't like each other enough to share our territories OR our companions/flockmates with each other"...So once that jealousy over territory is removed, and once you start spending time with each of them one-on-one each day and they no longer feel that they're sharing you either, you're will likely have not only two very happy, healthy, loving birds, but two birds that are BOTH closely bonded with you finally...The female's past and current behavior is being forced by her dominant personality, coupled with the fact that she just doesn't want to share her territory or her "person" with that other particular bird...But that in no way means that she doesn't want to be closely bonded and loving with you, but you first need to remove the current stressor that is causing her to behave the way that she has been...And once you do that it's going to be a whole new ballgame...
And you have my number if you ever need pep talks, okay? Stay patient and loving with her and don't forget that parrotlets do bite - it might happen a thousand times again, but don't react or that reinforces the negative reason she bit in the first place. My parrotlet Coco alternates between snuggles and kisses and then charging me to taste my flesh. Her attitude is one of the many reasons I love her so!
