Agreed. No common IT infrastructure means months of headaches in implementation, especially if one of the divisions has a much higher security than the others.
HQ and the three "autonomous" divisions need to pool their IT resources together first and make sure that whatever solution(s) they come up with is really usable across every organization. There needs to be a commonality across what is supported both internally and externally before even thinking about what the best solution is. Then you've got security across the four entities to consider, any and all legal implications, disagreements between the IT departments...ugh.
This is a huge undertaking, and I feel bad for you. Good luck anyway.