Yes, you can get to the Altun Ha or Lamanai ruins in one day, and do the cave tubing in another day. I dont believe you can do both in one day.
Christmas and New Year weeks are a couple of the busiest weeks in the year. Most hotels are booked in advance, certainly the nice hotels are. So, that means lots of people, or seemingly lots of people for us.
There is sometimes a concert in the central park, Santa comes to visit the kids with LOVEFM radio, Nurse Donna at the Health Clinic also usually does a party for the island kids.
Many restaurants on Caye Caulker are closed on Christmas day, or at least in the morning, so you might want to get to the bakery the day before. The banks are closed and most of the time the ATM will run out of money before the holiday ends. This year Christmas is on a Friday, and Boxing Day is on a Saturday, so the bank will not reopen until Monday, and could even be closed until Tuesday, they will have their schedule posted the week before.
Also, Bowen & Bowen, who distributes the water, beer, soda, etc. is closed, so make sure you have plenty of drinking water. The stores sometime run out of essentials like drinking water, flour, sugar, rice, since the supply barges do not run during the holiday.
The water taxis keep their regular schedule and sometimes add additional rins depending on the demand.
Prices remain the same whether there are cruise ship passengers in town or not. Caye Caulker does not get many cruise ship passengers anyway.