Does Steam family sharing work on different computers

Yes. You may authorize Family Library Sharing on up to 10 devices at a given time, and for up to 5 accounts that may then use your game library on any of your authorized computers.

How do I share Steam games with family on different computers?

From the Steam Settings panel select the Family tab . Here you can select users who have also logged into this computer to share your library with. Click the "Authorize Library Sharing on this device" switch. Check the box next the account you'd like to share your Library with.
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Can you share a Steam account on 2 different computers?

Yes, you can run your steam games account on any PC. Just log into steam on that PC with your account. We have many PCs in our family, with steam on all of them. I have my account logged in on both my laptop and desktop.