Nice to see some familial generosity. I'm slightly confused though, when you log in using her account you're not able to delete the remaining admin account (your old one) right? Becuase obviouslly you cannot delete an account you are logged in under.
My initial thought is - upgrade to Jag, either archive all old accounts, or just do a clean sweep and start from scratch. All those old G3s work so much better under Jag, and I have also succesfully deleted admin accounts, including the original admin account (ie the one which originallly was created on the installl) in Jaguar. Why it won't do this under 10.1 I don't know.
Upgrade now before she has used it too heavily, that way you could do a clean Jag install - and you don't need to worry about your old data.
Assuming you can't upgrade, because you don't have the disks, or your new Jag system disk is DVD, and your old G3 won't run it, so you have to use 10.1, then try to delete the old admin account when logged in as root. You'll have to enable the root account, but there are many instructions about how to do that, and the slight danger which accompanies it.