Oh my.... Wonderful vacation, but it will be very busy with two little kids so close in age... I just do not know if I would be hauling all of those things. Especially with the new luggage limits. Now, I do have a little germ phobia about rental car seats and LITTLE kids, so I do think I would bring my own car seats. I would actually check the 1yr old's car seat though; since it sound as if you did not purchase her a seat on the plane, so no need to lug it. I would lug the toddlers though on the plane. It will keep her more content, less busy and more secure. Trust me, we have traveled California many many times (going again in March whoop whoop)! That is a 4hr plane ride and they travel better in their own seats on the plane. Bring plenty of snacks, activities, games on the plane. ALWAYS have a NEW never seen toy that you KNOW will be a big hit for your toddler. This works great on that 4HR ride. Now I would pack the snacks and entertainment stuff in a backpack and have your toddler wear her own backpack.
I would wear my one year old in a sling if you have one. Gives you free hands for your carry on. I would bring my own double stroller, although they can be rented at all of the locations/attractions you mention, but none are the recline type for naps. CHECK your double stroller underneath the plane. Makes getting through security easier. If you do decide to bring it on the plane though, they will gate check it. I just always liked the less hassle through TSA as possible.
I always bring a themometer with me and small bottles of medication essentials. Tylenol, Motrin, tummy stuff. I actually bring this on the plane. I also would purchase something for them to drink once you get inside of the airport. Helps with take off and landings. Drink boxes work great.
I would NOT bring folding high chairs. By that time your 12 month old will be a lot bigger and your toddler will be 2 1/2. At the house/resort your toddler can sit in a regular chair for meals when eating there. Out in the restaurants there are boosters. If you find yourself needing a booster for your 1yr old at the house and the house does not have one, it is cheaper to run to Walmart (you have a car) and buy one of those cheap boosters than what you will pay to add on luggage at the airport. Then you can even leave it there for the next family. Whoop Whoop. So leave the booster chairs at home.
Now you are not going out of the country, so you do not need any major documentation. With the new safety on the airlines, the BC are fine (my kids have passports so we do not carry BC's), but they are not needed. THe only time you need BC's are if you are going out of the country or to prove to the airline a non-ticketed child is under 2 yrs of age. You have purchased a ticket for your 2 yr old and your 1yr old I am sure will not look 2. If you want, you can carry them and I would carry them with all of your travel documents/ID's/tickets on your carry-on. You do NOT NEED medical records or immunization records. Remember if something were to happen you are still in the states. So no other paperwork is needed if you do not have children with disabilities.
Do not forget the sunscreen and sunhats and you are good to go. Remember they have stores there. Even though a little more spendy and the fact they have tax on clothes(AHHHH!!!) you can get any forgots there. Just relax and have the best vacation ever. Have fun!