Hi,
We went to Fiji a couple of year ago. We stayed at the Outrigger. Most places have kids clubs but depends on what age your kids are. I think it's if they are under 3 you have to send them with a babysitter or an adult has to stay with them. Babysitters are very cheap.
Fiji is very relaxed expect a very relaxing time. We went from memory for 6 nights and that was really about 1 or 2 night too long.
Passports you can do all forms online and then all you need to do is print them and sign and take to the post office with your photos. I have had to get a few passports and all of them we have received within two weeks of lodging the paperwork. Below is the link to do the passports online.
We did not need to get any vaccines you only need them if you are going bush walking etc or in th forest.
Hope that you have a great holiday. Nice place to go but not much good for shopping but great for relaxing.
Passport Application