From what I know, I'm pretty sure that a cockatiel feels like she's being threatened basically if someone or something goes near her cage area. Her cage is like her little area, and allowing your budgies to play and go and use her cage is not acceptable(no matter how adorable they are) it isn't going to coerce your cockatiel into liking your budgies or for that matter start liking you for giving her a friends to play with. If your birds are tame enough, I would suggest letting all your birds play in a neutral area and giving out treats or toys that everyone would like.
My Budgies and Cockatiels have bonded well enough for me to understand that they can live together and be friends, they are actually sad that they live in separate cages and only get to play together, but every bird has its own needs and desires.
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