how can I rerender a whole row in a datagrid? - jsf

Question

I have the following code, using PrimeFaces 3.0.M3, Tomcat 7 and Mojarra 2.1.3.
<p:dataGrid columns="1" var="answer" value="#{answersbysubject}">
<p:column>
<p:panel columns="1">
<h:outputText value="#{answer.question.name}" />
<p:dataGrid columns="5" var="selection" value="#{brain.selections}">
<p:column>
<h:panelGrid columns="1" styleClass="selections" id="mySelection">
<h:outputText value="#{selection.name}" />
<p:commandLink update="mySelection">
<p:graphicImage value="/img/CheckboxFull.png" rendered="#{selection == answer.selection}" />
<p:graphicImage value="/img/CheckboxEmpty.png" rendered="#{selection != answer.selection}" />
<f:setPropertyActionListener value="#{selection}" target="#{answer.selection}" />
</p:commandLink>
</h:panelGrid>
</p:column>
</p:dataGrid>
</p:panel>
</p:column>
</p:dataGrid>
sorry if a bit too verbose...
The point is: I want to realize a nicer 5-way checkbox (working like a set of radio buttons).
The whole works fine serverside, except that when I click another checkbox it rerenders ONLY the checkbox I just clicked. That is, I see two checked checkboxes - the old one doesn't clear until I do the F5 refresh in browser.
I tried to give ids to each tag and then let the commandLink update all, but nothing else than the current checkbox gets updated :(
The ids of a table row get probably mixed up during dynamic generation, is this why no other tags can be found/identified reliably for update? If this is the situation, then what would be the solution for me to update ONLY the current table row (not only the current table cell like now...)?
Many thanks!