They do make three year vaccines, HOWEVER, many vets do not carry them because they have not been on the market long enough to show that there are no other problems with them. (does anyone remember the heartworm shot?) Also, they have already shown that cats who get these 3 year vaccines have an increased risk of having an allergic reaction or, worse still, developing a type of cancer at the injection site due to more adjuvants which are what help make the vaccine last longer.
I personally think the safest thing is to due is titers on your cat. They are more costly then the vaccine, but at least your not putting unneeded chemicals in your babies body. Most states that require rabies vaccines will accept having rabies titers done.
Finally, if your cat is being exposed to another cat who is outdoors and you do NOT know if the other cat is leukemia or AIDS positive I would either get you cat vaccinated for it or do not let them play together. Leukemia is transferred through saliva and all it takes is for the other cat to sneeze, hiss, or even drink out of the same water bowl as your cat to get it. AIDS is a little more difficult to contract, and mostly requires contact with the blood of the affected cat. (bites or scratches) Your cat can NOT get anything from the dog so I wouldn't worry about that one.
I do agree that you should have your pet examined at least once yearly if they are under the age of 8. If they are older it is best to take them for an exam twice a year and preform a full bloodwork panel (inculding T4 test) once yearly. Remember that your pets age MUCH faster then you. By the time there 8 in human years, in cat years, they're nearly 60's! When you're 60 are you going to wait 7 years in between your doctors visits? A LOT can change in one year for a cat so it's best to catch things early before they become a MAJOR problem.
Best wishes in deciding what to do.