Forgive me if I'm missing something here, but: a suggestion less drastic than some of the above.
Right click on the MSM icon in the bottom right corner, then select "Sign out."
One of the options for MSM is to sign in automatically, i.e. when the computer is switched on. If you deselect this option you won't have the problem.
However, unless you have separate accounts, it means that your daughter will have free access to all your files and applications.