The "Adobe product license agreement" for "Adobe Reader" (at http://www.adobe.com/products/eulas/reader/x/eula_en_gb.html) says:
3. Software License.
3.1 General Use. You may install and Use one copy of the Software on your Compatible Computer.
I imagine that this restriction is meant for Adobe's paid software, such as Adobe Acrobat itself (rather than the free Adobe Reader program").
However, I thought that I ought to verify this.
Is it OK for my family and I to use the Adobe Reader concurrently on several different home PCs?
Actually with Adobe's paid software you can use it on up to two computers -- but the clause you cited can also be read as "one copy per computer," so no worries - your stated usage should be fine.