This is a pretty tricky problem. I'll try to explain what I would do, but it will be tough without actually having a similar report in front of me.

First, I would create a report that groups by Name. In the Group Footer, create a subtotal for the number of records printed for that person. Thus, this will tell you if that person is just the member of one group, or more than one group.

Second, hide the Details section b/c you don't want the individual records printed on the main report.

Third, create a subreport in the group footer which is passed the subtotal field and the category to be printed. Using logic in the Suppress property's formula workshop, you will need an involved formula which checks to see what the user selected (Group1, Group2, or Both Groups) and the subtotal value. Something like this (you will have to work on this to get it actually working in your report):

Shared NumberVar NameSubtotal;
Shared StringVar TypeOfReport;
if TypeOfReport = "Group1" and NumberVar=1 and {table.field}="Group1" Then False; //don't suppress

Do this for the other possible combinations of report types. It will take some time to get all the combinations figured out, but I think this is a way for you to get your report working.

Brian