My condolences for your lost data. Unlike computers, there's no way to "undelete" data on a console. Once it's deleted, it's gone forever!
To make matters worse, Mario Kart Wii's safe file is copy-protected (as noted on Page 4 of the game manual) due to online multiplayer support, so there's no official way to make any back-ups either.
Unofficially, there's two ways to back-up such data... but it requires you to modify your Wii (WARNING: VOIDS WARRANTIES) & use a homebrew back-up method.
First option is the SaveMii tool within BootMii (which create a snapshot of your Wii's internal storage at that particular time) that can be use to effectively "roll back the clock" on the system with the RestoreMii tool... but this can be lengthy (around 20-30 minutes for SaveMii to create the back-up, around 5 minutes for RestoreMii to make the necessary changes) & does the entire system (as an "All or Nothing" deal), so you cannot choose what gets changed.
Second option is GaveGame Manager GX, which allows you back up & restore any game (even copy-protected ones) to an SD card or a USB storage device.
HOWEVER, much like PC back-ups, they have to be made BEFORE the damage occurs... which is the sad truth here.
The only other protective measure (which is a bit late to protect your lost data, but may protect other stuff) is to go all out on the parental controls & lock down everything. I know you'll have to enter your security PIN any time you want to play a game or do anything drastic, but it'll present a roadblock to anybody who doesn't have that PIN.
Normally Nintendo places obvious warnings about data not be recoverable in these situations, but a quick require of the Mario Kart Wii Manual & the various versions of the Wii Operations Manual as well as the Channel & Settings Manual... instead of resorting to on-screen warnings generally asking you to confirm your decision (as you generally have to hit delete two or three times before goes through).
I know this isn't the answer you want to hear, but it's the harsh truth that you'll have to live with. I understand the pain of losing a long-standing save file, having lost a save file on a Pokémon game with over 500 hours logged due to the death of an internal battery. Just get through the common steps of grief, make some contingency plans (to minimize risks in the future) & move on.