In my experience, cats and raccoons will generally ignore each other -- my cats and the neighborhood fauna all ate on the porch together for years with no inter-species altercations whatsoever. With rabies now, though, all bets are off.

Raccoons were not averse to unloading the garbage in our kitchen when the humans had stepped out and left the doors open, but they would generally leave if you suggested they go out the way they came in. (The cats' function in these cases was generally observatory, if they happened to be awake at the time.)

You may find that once the kids have grown up and moved away, your problem ceases (at least until next year), since mama isn't scrambling to fill little mouths. Would suggest rather than attacking a captive with a water gun (and possibly freaking it out), try coaxing it toward the exit with a trail of crackers. They mostly just want chow. This will not solve your cat door problem, but keeps the peace in the short term. Then wash anything they've been eating out of with a 2% chlorox solution, just to be on the safe side.