Is there a way to transition from HPDE 1 to HPDE 2 on the day of the event if the instructor feels we are competent?
Yes. There is no time requirement for progressing between HPDE groups. It's all dependent on driver ability (based on what an instructor assesses).
2. How can two people share a car in the same class?
You can't really. Techically, one person could drive the car for half of the session, come in and the other take over for the next half. However, counting cool down lap and driver change, you'll lose a lot of track time trying to share the same car in the same group.
Most regions will run HPDE 1 & 2 together, then HPDE 3 & 4 together. With that, if you want to split you and your wife into two groups it has to be groups that will run separate to make a single car work. Given your experience, you could probably split one of you into HPDE2 and the other into HPDE3. The first session or two, no one is running that hard (and it's HPDE, not racing so it doesn't matter if you want to take it easier compared to some).
I'm assuming you are looking at Gateway next month? We haven't got the schedule planned yet, but but HPDE is typically split that way.
3. Can we register 2 cars? We have a Cayman S and a mildly modded CTSV wagon. I will have appropriate brake pads on both. To be honest we would prefer the CTSV but if 2 people cannot share a car equally I will grudgingly let her drive the CTSV and I will suffer in the Porsche!
Entries are typically by person (i.e. two people, two entries, two entry fees). So regardless if the two are sharing a car or each have their own cars.