You basically have two options, and a third secondary options. In my personal biased order of interest :
1°) Airborn infantry. Conquer the main island city, annex and repair the airport, rebase an airborn infantry, then use aerial assault to jump from island to island. It's quite quick and doesn't mobilise for too long your units
2°) Marine infantry. As they can disembark everywhere, they are able to conquer those little islands. Quite slow in my opinion, due to the 4,5 hours / 3 hours to enter and exit each location.
3°) Ignore those little islands, make peace with the AI. Those islands are very minor.
Running an online alliance is pretty much like running a small company, except you need to find other way than money to keep your employees productive. May they play or work, they are humans.