Several options come to mind, if I'm understanding properly, depending on one's specific needs (shapes to be cut and the like). I'm not sure I have a complete view of what you're trying to accomplish, though.
If the goal is not through holes but just removing reinforcement material on the inside without going through the outside skin, a router with the depth adjusted appropriately is about the best option I can think of. The base plate is the key here to controlling things. Just manipulating a router bit completely freehand would be very hard to control (as it sound like you have already discovered). The Dremel router attachment would probably do okay here.
For largish round through holes, a hole saw in a drill would probably be tough to beat. For smaller ones, obviously one uses a plain old drill bit.
For mediumish to reasonably large through holes with straight line sides, an oscillating multi-tool would be good. These are remarkably handy, not the fastest cutters in the world, and can do some cuts that are pretty much impossible to make otherwise.
A jigsaw/saber saw would also likely do the trick for through holes, though may tend to leave somewhat rough edges.
