Steam: share games within family. Library locked? [duplicate]

I have bought a couple of games on steam for my kids. Everything worked great until I bought another computer for them. So now I have 2 computers for them to use. I thought that login om same account they could use both computer as long as they not played the same game. That didn't work. So I created another steam account and used familysharing to share the games between the two computers. That did not work either!! As soon as one computer used ANY game on the "library" the other computer could not play anything.. what the heck!

How am I supposed to let my children play som games from steam without buying multiple copies of every game??!!

I found something about creating multiple libraries. But for that I need to partition the hdd for each library which would contain only one game each. Can that be an option? If I create multiple libraries will they all be locked while sharing to another computer?

Please help me. Many people (parents) must have this problem??

Should I create a new steam account for each game??

Thanks!