I have downloaded the application. All is well until I try to open my page. At this point my daughters page opens in my account.
Any ideas ?
Assuming you've installed Skype from the .dmg file, all you need to do is sign out of your daughter's account and sign in with your username and password. When Skype is running, click on the File dropdown menu (third item from the left at the top of your monitor's screen). Sign Out is the last item in the list.