Leslie, just signed in to reply to your message. I used to work for the RHS and attended many Chelsea shows in the line of duty. Its a great day out.
Yes you can see it all in a day. Some parts I suspect will be more interesting than others. I imagine your priorities will be the two big marquees where the nurseries have their displays, and the show gardens. Of less interest I suspect will be expensive garden furniture, very expensive sit-on lawnmowers and even more expensive greenhouses. I'm sure you've got plenty of that sort of stuff in the States. There are lots of stalls selling all manner of gardening kit and some secondhand book sellers. Also a flower arranging marquee and a hanging basket display.
I am pretty sure that the tickets are only valid for one day. This was certainly the case for the complimentary ones issued to staff. So, if you did want to go back for a second day, you'd need another ticket. (Messagers should correct me if I'm wrong, I've never actually seen a ticket that someone's paid money for).
Get there as early as you can, its busy right from the start but slightly less crowded in the first part of the morning. It can be a real battle to see the show gardens once the crowds build up. There are plenty of places to eat and drink, but it can be hard to find anywhere to sit at lunchtime. If the weather is fine I used to enjoy sitting and listening to the band. Take some form of weather protection: if it rains, the show turns into a sort of umbrella hell.
Everything is set up by Sunday, which is when the judging takes place. This is definitely not open to the public. They do it on Sunday so that the awards can be on display for the gala the next day.
Monday is gala preview day, when the celebs and royals turn out. I think that is already sold out.
Tuesday and Wednesday are members days and since you are a member, I recommend going on Tuesday when its at its freshest.
Thursday, Friday and Saturday are open to all.
Sell-off is at closing time on Saturday. I am sure APHIS (American Plant Health Inspection Service - lovely acronym) will not let you bring plants back into the States, so I should forget about that. Anyway, its all looking a bit tired by then. Its also worth remembering that a lot of the plants are out of season and forced on, or held back, by every horticultural trick known. Their chances of survival once you get them home are not good. The sell-off is however one of London's more surreal sites, as the punters totter off down the Chelsea Embankment clutching eight foot high delphiniums.
Have a great time!