Well, the App Store won't allow other IMAP clients as a matter of policy (you're not allowed to duplicate functionality present in native apps), so unless you jailbreak you're not going to find a 3rd party client on the App Store.
The simplest solution to your problem would be to just passcode-protect the iPad so your daughter can't access it.
One alternative (if you don't like your existing webmail) might be to use a 3rd-party webmail client that lets you just check your IMAP email using a web interface. Sadly, Gmail will only do this for POP3, but after a quick Google, it appears some of the links on this page may be useful for that purpose (though I can't vouch for any of them in particular). Mail2Web and MyEmail seem to be the least-obviously-bad choices there.
Anyway, that would add a layer of security between your daughter and your email, effectively substituting for the 3rd party client application you're looking for.