Hey smokin Joe,
With these current conditions, and after reading of current reports of the trail, it would be very difficult to reach the summit. The 99 switchbacks from trail camp are still covered in snow and I believe people are climbing up the chute and switchbacking back down or glissading down with an ice axe.
Is this your wife's and son's first whitney trip? If so I recommend camping up in whitney trail camp but it's risky to reach the summit in that setup. If both are doing a one day gig of reaching the summit, it will take much longer anything above 9,000ft where there's still snow covered.
In my opinion, it's best to hold off till the end of the month or early July. I'm going up June 29th for the weekend but preparing to use my crampons and Ice axe if necessary..
Amazon tends to falsify with some gear online but it looks to me those are microspikes which are great when there's small compact snow which I can see myself using up on the trail crest and summit trail.
Hope this is a good reference, enjoy and good luck!
