You might need grounds to exile them. At least, you might need grounds for the public to see that as a reasonable step.

> What are their grounds for the power they currently wield??

In this case...Constitutional.

If you are going to do it legally, yes. I presume whoever escorts them out of the palace will want some legal authority to do so.

The grounds for the power they currently wield is that it’s the law.

You definitely need grounds to exile them / strip their wealth.

Taking away their political powers / their status as royals is one thing, but exiling someone is punishment. You can't just hand out punishment for no good reason.

If they commited crimes that were illegal at the time they were commited they should stand trial for that, but I very much doubt any of those are serious enough to warrant exile.