Hi Blakey,
Assuming that you would be going through a provider for connectivity between main router and sites.
1) Find RTT from main router to sites
2) Find RTT from sites to main router.
Again, if you have a monitoring tool in place, a baseline generated would give an idea of what the normal RTT should have been (before the problem). It should also indicate any packet losses. With these results in hand you could go back to the provider.
HTH
Lejoe