My sister and I keep switching skins in minecraft!
Solution 1:
This is an unresolved bug.
Please consider researching the topic a little more before you post here. In this case, you can find the linked page on the 1st result by searching minecraft bedrock skins switching on any simple search engine.
I understand that you did do some more research on the topic, and that you have found items talking about the bug but not fixing it. In that case, I would just like to confirm that no, there is no current fix, I'm afraid. You'll just have to go on without it. I'm terribly sorry about this bug.