Hi Lauren,
Taming a new bird takes a lot of time and patience. When you want a bird to be a tame pet, it is best to only have one bird in a cage. It is going to be very difficult to tame your budgies if they are sharing a cage. Birds will always choose another bird as a companion over a human if given the chance. It is just their nature. If you want to have a better chance of taming them, they need to be in separate cages. And even once they are tame, if you put them back together, they are likely to stop wanting you to handle them. Once a bird bonds with a mate, they don’t have physical contact with other flock members. You will always only be a flock member. So each bird needs to look to you for companionship, not another bird. They also need to have their wings clipped by a professional, because if they can fly away from you, you will not be able to work with them.
Please click this link and there are articles about bird behavior and taming and training that should help.
Caring For Your Bird
Thank you for asking Lafeber,
Brenda