I, too, think this scenario less than credible.
Not only would it take the resources of something akin to a nation state to bankroll and implement such an invasion, but whoever attempted it would be faced with the dilemma of providing material support over a huge distance (there are no credible sources of such an invasion close at hand) in the face of a blockade put in place by a modern military and those of allied countries.
It's hard to think of a scenario in which the Canadians - as a free, democratic nation - would not recieve some support from allies.... and even harder to think of a realistic scenario in which a non-state actor would not be subject to restrictions, if not outright attack at whatever place they use as a base.
OK...
First, establish a blockade. PEI is probably self-sufficient WRT food, but little else. So your invaders are denied resupply of fuel, equipment and spare parts.
Secondly, it is *highly* unlikely that a group such as you posit will have the equivalent technology to that possessed by Canada and her allies. Therefore I now make it my business to destroy all of the invaders' aircraft, radar and radio communications.
The invaders are rapidly reduced to the level of a third-world army without the capability to easily detect incoming assaults, or respond rapidly to them at above unit level. They are unable to operate in the classic guerilla fashion, because they cannot blend in with the population, and are unable to attract the sympathy of the population.... because you have them effectively using the population as hostages. Bear in mind that the vast majority of the PEI's population are of anglo-celtic background, so it's unreasonable to argue that the "rebels" will have popular support.
Therefore, I suggest that the Canadian armed forces will be able to establish a beach-head on the Island, and eventually retake it, more rapidly than might otherwise be considered.
Beg pardon if I suggest that this scenario is not reasonable , unless
led by Peter Sellars, complete with Q-Bomb.
nfloorl:
http://http://en.wikipedia.org/wiki/The_mouse_that_roared
<edited to add>
Preliminary to establishing a beach-head would be the insertion of recon and raiding teams. Recon for gathering of intel (obviously) and raiding to both destroy vital equipment and to also gather intel via taking of prisoners and observation of the invader's reaction.
The establishment of a beach-head will also force the invaders to concentrate in such a way that they can be more easily attacked with high-tech and heavy weapons.
IMHO, a force such as is postulated here cannot hope to hold an area such as PEI in the conventional sense. Nor can they hope to do so via an insurgency or guerilla war. Effectively, their only hope is to hold the civillian population hostage. "Fight us and we we start killing your people!".
The other issue that has not been addressed in this scenario is the reason for the invasion. There is no currently plausible reason for a rebellion to arise. Nor could it do so successfully, spontaneously and in the short term without the Canadian national government responding. PEI has no known economic or industrial assetts that would make it a tempting target, and making that worthwhile would require the ability to export. Kind of hard when the most obvious first response by the Canadians and their allies is to blockade the invaders.
The problem with scenarious that are as unrealistic as this one, is that they become too dependent on arbitrary decisions by whoever is creating them, and also too dependent on unknown factors. Perhaps they belong on a fiction board, rather than one devoted to real-world military issues.
Regards........... Peter