- one family picks up permit, hikes up to camp at Lone Pine Lake or Outpost camp
- second family hikes up Thursday a.m. to meet us and we continue to Trail Camp together
FYI Lone Pine Lake is not in the Whitney Zone, so I'm not sure your Whitney permit allows for camping there. It's really not that far from the Portal to be worth stopping there anyway. There might be a different Inyo Forest Wilderness permit needed.
Your permit start date is the date you enter the Whitney Zone, not when you leave the Portal.
I'm pretty sure the permit rules say the whole party has to be together as a single group. So starting at different times/days would be against the rules. If a ranger stops you and you're not together, it could be a problem (and I have been stopped by a ranger on the trail). Maybe beeing spaced out a little will be okay, but hours apart will probably raise some ranger eyebrows.
- one family picks up permit on Wednesday, does acclimatizing hike to Lone Pine Lake or Outpost, return to sleep at Whitney Portal, everyone hikes Thursday
Nope. If your entry date is Wednesday, that's the day you have to start and enter the Whitney Zone. Even if it's 11:59pm Wednesday.
Once you leave the Whitney Zone towards the Portal after your entry date, your trip is over. (they might not be able to tell, but it would be against the rules AFAIK) I don't think it would matter if you enter and exit and reenter on the permit entry date, but if the clock hits 12:00:00am Thursday and you're not in the Whitney Zone, you're breaking the permit rules.
