Gamertag was changed on the wrong account.

If it truly was a glitch that sux. Only way to try to fix this if possible is to contact customer support. I can't guarantee that they'll fix it. Its worth a try though.

Unfortunately no. All you can do is buy another gamertag change if you want to change it to something else.

I know, but the point is that I am pretty sure I was logged in to the correct account. I believe it was some sort of a glicth, as I did this change on a web browser, and I did moved around the page a few times, as I was trying to find the option to change the gamertag, and even then, when I've found, I saw my daughter's gamertag showing on the screen before choosing a new one. How could that be possible? One thing to mention is that I also added her to "my family" and of course, she does not have a Microsoft account. Anyway, I don't know what happened but I know that there was some error/bug/glitch, on the website that made me change the wrong account.

Hello sorry only option would be to pay to change. In the future please just be careful and make sure your in the right account. Double check before you try to pay.

Unfortunately, you will need to pay for the gamertag change.