Car rental to tour Normandy area. We will be coming from Hague/Amsterdam on train.

Dever,

You can either get the car in Bayeux (or nearby Caen, if the rates are better), or else in Lille. The two options seem to take about the same amount of time (most of the day).

It looks like there are cheap flights to Rennes, but I have zero experience with that.

If you are taking the train from Den Haag to Normandy, you'll be changing trains (and train stations) in Paris. So you could train to Caen instead of Bayeux if you find better availability (especially if you need an automatic) there.

I recommend that you include a one-day small-group tour of invasion sites in your itinerary rather than trying a 100% do-it yourself approach. Having a professional driver/guide will be more informative and more efficient. It might well save you a day's car-rental fee. It's a short train ride from Bayeux to Caen if you need to hop back over there to pick up a car.

Highly recommend a do-it-yourself car tour—despite the onslaught of recommendations you will get on this forum to only do an organized tour. Just read up on history and geography beforehand to get the most of your experience (this applies to those who take organized tours too).
More to your question as far as a rentals, I have rented cars in both Caen and Bayeux. IMHO, the convenience of the rental agencies to the Caen train station more than outweigh the time it takes to drive to Bayeux from Caen. That is, if you rent from Bayeux, you have to get from the train station to the rental office (which is not at the train station). By the time you have done this, you could have just driven from Caen to Bayeux. Plus, there are more direct trains to Caen.

From Den Haag to Lille by the fastest train connections take 2.5-3.5 hours with either 2 or 3 connections, at least one of which is by reserved train (Thalys, TGV, or even possibly Eurostar). The Belgian rail site sells tickets for that whole route. You'll still have some driving to do, but by any route or stops that you like. Cheaper to book ahead because of the fast train.

From Den Haag to Lille by unreserved InterCity trains takes 5 hours with 3 connections and costs only 55 euros per person in 2nd class. Same price whether you buy on the day of travel or in advance. To buy the all-IC options on the Belgian site, you have to add a "Via" midpoint of Tournai. You have less of the afternoon left for driving, but that's probably fine if you have no evening plans in Bayeux. (I first found these schedules on DeutscheBahn by requesting a route "without ICE," meaning without the fastest category of trains.)

To get all the way from Den Haag to Bayeux by train, I'd probably choose a route including a direct, reserved Thalys from Rotterdam to Paris Nord station, and a connection at each end, plus the change of station in Paris. Travel time 6-8 hours, depending on the actual connections. Book at least the Thalys leg in advance for the best rates. Paris to Caen or Bayeux don't require reservations but advance-purchase discounts will still lock you into a particular train; this leg is sold by SNCF and other agents, not on the Belgian site above.

I trained to Rouen. Then rented a car there and started my Normandie sight-seeing in Etretat and Fecamp (and worked south).

For D-day sights, Caen or Bayeux will have rentals. If staying in Bayeux, and you're not planning to see sights on the way, you might as well rent there after you arrive.

Mt. St. Michel is only about 1 1/2 hour drive from Bayeux.