Wait, Steam offers you a "share library" feature but then locks your account when you use it?!

Not as in an account ban, it just only lets one copy of the game in question (or one game total? Haven't used it much) run at any given time. No different to lending your friend a Nintendo cartridge, except that it requires less running around. :)

Only one person can play from your library at once. So you are essentially lending the whole nintendo.

The frustrating thing is just that I cannot play free games on my steam account (hi dotas) whilst lending a paid game to ma famile.

They've fixed that. I had the same problem a few years ago and now if you properly add the game to both libraries it works fine.