Lovebirds?

Like the old saying "Birds of a feather flock together." Well that is what is happening. When you have one bird they will give all of their attention to the handler but when another bird is introduced they will drop the handler fast and attach to the new bird sorry to say. even if you keep them in separate cages which will really escalate the birds anxiety level and the birds will call to each other to no end. If you do plan on keeping them and having a breeding pair do your homework. They will need a large cage a flight cage and a nest box and nesting material for lovebirds. An appropriate diet for breeding pairs is needed also. Good Luck!

The bird-to-bird bond is easier than the bird-to-human bond.  This is something that happens when you have two birds; neither one is so dependent on you.

Tips? Keep working on it.  Get them to take food from you.  Talk to them.  

Also, it is now Spring, so they may be thinking of starting a family.  You might cover the cage to keep them in the dark at least 13 hours a day, as if it were still Winter.  It should keep them less hormonal, so maybe they will be more open to your friendship.  If they start mating, they will become very protective and may want to keep you out of the cage too.  

Get rid of your parents. The bird bonded to the other bird and doesn't need you now. 

She is naturally more bonded to her mate than to you.

you could try seperating them