Were your wife and kids accounts set up with passwords for each of them or just names?
I haven't messed with multiple accounts on W 8.1 yet, but it is my understanding that the first profile used to set up a new machine becomes the administrator automatically. Others can be added with real MS hotmail/outlook accounts
and have remote access from anywhere from other devices if desired or dummy users can be set up with no real account that can be used like the "Public" account in W-7.
In 7 I set up an admin account requiring a password to make changes that require Admin authority but run the pc in general on individual accounts to protect it from outside access by bad guys. That means if I try to change something while in a normal user account I have to enter the Admin password to do it, but I think that is a small inconvenience for the extra protection added.
Each one had their own password. From what I was told by tech support everyone needs to an admin. I had the same issue with a gateway laptop I bought a couple months ago for the kids to use for school work. It was supposed to have the issues fixed by then and setting up the other accounts was a different process from what I remember. Yet the result was the same, it just lasted about 6 weeks instead of about 2 days like my desk top did 10 months ago.
For the reasons you listed, I have always set it up with only myself as the admin. One of our IT guys where I work has had the same issue with his home computer, he hates 8.