I only ever seem to catch them in the act of filling the hole, but never catch them chasing the gopher. And no matter what I do, I can't seem to find a magic way to get them to chase it. I really want to get that goal already.

Have you tried searching the original Virtual Families forum? The method for achieving the "Go-pher it!" goal in VF2 is the same.

For tips on how to perform a Search see this thread.