1. you apparently have no password on your admin account. if you want to keep your children from running system stuff, you should define a password. Then the UAC will ask for that.
2. some programs require to be run as admin. You can set them to always run as admin if you right click on them (best in All Programs), go to Properties > shortcut tab > Advanced > check the box in front of "Always run as admin" > OK > Apply (do not forget Apply - else it will not set it).
3. If normal programs like e.g. Notepad need to be run as admin, then there is another problem that we'll have to investigate.