"I'm sure I'm not alone with this problem!"
By no means!
Brief explanation:
There is *always a master admin/root account called "Administrator" - this is created during installation and has full admin/root privileges .
* the name of this admin/root account is "Administrator" by default - to increase security it is possible to change it to something harmless looking like "Jim" or whatever - I wouldn't bother in your situation.
This account is never shown on a normal login screen, only if you boot up in Safe Mode. In a default XP Home install "Administrator" may or may not have a password - installations vary, but usually not.
I suggest you login as "Administrator" from Safe Mode (just press Enter at the password prompt), go to Control Panel/User Accounts and change the "Administrator" password. Anything non-obvious will do - best is an easily remembered passphrase like "A Hostage 24 Tune" (a hostage to fortune), mixing capitals and lowercase and numbers. Write it down and put it in two safe places where you, but not youth X can find it.
Now for your account. Logout of "Administrator" and login normally as "Cheerio" (or whatever name you use). Check that your PW is non-obvious (Cheerio is a bad choice!) - pick a passphrase as above and write it down somewhere where youth X can't find it. The kids know your old one by now, so do change it.
Create a new, limited account for the kids. Don't bother to assign a PW.
See how they get on using that account.
Be warned that some carelessly written games (and some other apps) may not run. They want accesses to system files which is not allowed if started from limited accounts.
This is a big problem in XP that Vista, the next MS OS is "supposed" to address.

There are ways round this in XP, but they are all difficult, involve a LOT of fiddling and are distinctly non-obvious.