Hi Terry,
An Alexandrine is a much large bird than an Indian or African Ring neck, so yes, do not cage them together or leave them out together unsupervised. You don’t want to come home and find that she has killed him. There is no way to force birds to get along. They are different species, so they aren’t meant to interact. It sounds like she gets jealous of him being handled by you. She may have been content with minimal handling, but it was how she chose to bond with you. That doesn’t mean she likes seeing you handle another bird. So be cautious about their interactions and keep them apart when you can’t supervise them.
Thank you for asking Lafeber,
Brenda