Your dates are still several weeks away, and a lot can change in terms of conditions. The snow pack in the Whitney area seems about average, and typically by late June crampons are needed only thru the switchbacks in the early morning. The best advice I can give you is monitor the trip reports on the two Whitney BB's for conditions. And I'll put in a plug re: trip reports - tell us what the conditions are! It's fine to hear you had a great time, and cousin Johnny kept you up all night snoring, but ... give specific info about snow levels, ice, etc.
At this point, plan on crampons unless it's reasonably certain the trails have melted out. And, bring poles, but as for an ice axe? Do you know how to use it for self-arrest? If not, then only bring one if you plan to use it as a brake when glissading, as otherwise it's unnecessary weight.
Hope everything works out and your group has a great time.
