Wait, couldn’t have Allura used her ice powers to either brainwash Izzy to becoming a spy, turn her into an ice statue and trap her there, banish her and seal off the cave or better yet, actually try to kill her since she has sharp claws? Banishing her over and over and over really wasn’t the smartest plan for her to do.
Simple explanation. Allura’s hinted to be less evil than she appears, thus she didn’t want to take a more aggressive approach to dealing with Izzy until her patience reached its limit.
Allura partially got her revenge on Izzy at the end, but now the New Mane 6 know about her refuge, which is much closer than they like. That means Sunny has to confront Allura, who has demonstrated that while she is not violent, she is paranoid and suspicious of others. We have a good idea that her actions are motivated by the desire to find her brother, then no means will be unthinkable. She needs the Nova charm to get out of Equestria and find her brother.
Izzy seems a bit dumber here, but that’s because of her indomitable spirit above all else, which makes her Pinkie’s successor and which her friends really appreciate. Allura hadn’t expected this, she didn’t understand how single-minded Izzy could be when she decided on something. Zipp and Pipp came to Izzy’s rescue, and they will no doubt bring Sunny in for a confrontation later on.
Sunny and Allura will meet, where misunderstandings, explanations - and some violence - will happen. In the end, the New Mane 6 can help her to find her brother and go home.