The slider on the side of the SDCard isn’t a switch - it simply forces a contact closed inside the card slot when it’s in the write-enable position. Poking around inside it might in theory be possible to bend back whatever has got bent out of shape, bit it’s going to be pretty difficult, not only to see what you’re doing, bit also to see what needs to be done.
For experiment you could get a cheap SDCard breakout such as this: https://www.ebay.co.uk/itm/2PCS-SD-Card-...
and either take it apart to see how it works, or even, if you’re up to soldering, use the slot to replace your siser’s damaged one.
I have one just like that eBay one, and looking at it carefully it seems you’d only have to unsolder the top from the board at a couple of points either side of the slot opening in order to remove the top cover. If your little sister will let you take her Nintendo apart you may be able to do the same on her card slot and hence fix the problem.
In fact I’ve just taken the lid off mine, and here’s what’s inside:
The contact circled in red is pressed by the write-enable slider against the inside of the metal lid (laid out beside) to make a contact. Your sister’s has evidently got bent. If you were to solder a short length of wire between the bottom connection (circled in green) and the metal lid it’d think it was permanently write-enabled.
Good luck - you’ll be her hero for life if you succeed!