Currently best readily available replacement is the R4i Gold 3DS Plus.
You might be able to enable usage of old flashcarts by installing custom firmware on your DSi https://dsi.cfw.guide/
Unlaunch disables most restrictions in the normal system menu ("Launcher") and can start cartridges on it's own bypassing Launcher altogether (does not work for all flashcarts and/or retail games).
A little warning: unlaunch applies some non-optional patches to Launcher not everybody likes… The "Health and Safety Warning"-screen is removed as well as music and sound effects in the system menu.
If you just want to test if you can re-enable your current flashcart you can stop after installing unlaunch. But replacing the normal Launcher with HiyaCFW+TWilight Menu++ is a very good alternative to flashcarts.
@Bunjolio, I don't really think your sister should be doing those things at a young age. No offense, but its likely possible that she got manipulated online?