Just to confirm, you are sleeping near MSM, and plan to visit the interior of the Abbey the morning after Night 4? Be sure to check days of the week closings and extra weekend traffic. MSM is not "close" to Bayeux.
How are you arriving from Bruges? I'm guessing by car. I ask because (while I am not remotely as interested in WW II as your family is) there are quite a few war sites along the Belgian coast. I think that's related to the enduring popularity (well, beach time must be a factor too) of the shore Tram line that originates in Ostend (a quick train ride from Bruges.) Because they are less-visited than Normandy, you have to look them up.
The other reason is that if you are coming by train (which is not very direct), our host Rick has a Rouen car-rental strategy that involves hiding your bags in the trunk (if you get a trunk) and NOT taking the car out of the big rental company garage until you get a couple of hours in Rouen. I haven't done this, and I would certainly make a backup plan, in case your rental car is out in the open in a lot, instead. Don't fail to check for second-country rental drop-off fees.
I have not been to Caen, but I would note that there are staggering number of indoor and outdoor WW II sites to visit in the vicinity of Bayeux. You will not run out of significant things to see, even if you can't get to Caen. If you have skimped on book research, you should certainly ask your private guide to write down a list.
Note that parking lots around the Omaha Beaches can be very crowded in July, and you may have to cruise for a space every time you move the car. But a car is essential for your particular plan. We chose our hotel partly for easy parking and returning. We only devoted one day to WW II.