Staying near Rotterdam en-route to Cologne and visiting Amsterdam

There are many options, but to narrow it down I am interpreting your question as follows:

• You travel from England to Cologne, Germany
• You want to stay 2 nights in NL and visit Amsterdam
• You want to minimize driving
• You will have a single accommodation for the 2 nights where you will park the car.

You will probably drive from Rotterdam, to Dordrecht, Eindhoven and cross the border at Venlo. Along that route there are two cities I would recommend staying at with a nice train connection to Amsterdam:

• Rotterdam
  • has a fast train (Intercity Direct) to Amsterdam which takes you there in 40 minutes.
  • Price is 19.60 one way (there's a 2.70 surcharge for the fast part).
  • If you stay on the northern part of the city, travel from your accommodation to Rotterdam central station can easily be done by public transport or by foot.
  • Rotterdam itself is also a nice place to see as in addition to A'dam (my opinion).
• Dordrecht
  • Smaller city, with a good train connection to Amsterdam (via Rotterdam, see above).
    • Alternatively there's a ferry from Dordrecht to Rotterdam which is (with non-rainy weather) a scenic trip in itself (+/- 14 euro for a day-pass).
    • Probably cheaper accommodation

If you're willing to make a small detour from the Rotterdam-Cologne route, I would suggest:

• Utrecht

  • has an intercity train to Amsterdam which takes you there in 25 minutes.
  • Price is 8.40 one way.
  • Public transport or walking is very feasible from your accommodation to the central station, if you stay in the city.
  • Utrecht is a beautiful city, but is more comparable in style to Amsterdam (my opinion).

• Amsterdam P+R locations

  • Relatively cheap and fast public transport into the city center
  • Some P+R locations provide charging facilities for EV's, but I can't find which.
  • You can find cheaper accommodation in a surrounding city, e.g. Amstelveen and make the short drive to a P+R location.

To check out other train journey prices/information you can use ns.nl, the site of the Dutch railroad provider.

As you mentioned that you're travelling with a group of 4 note that there are group tickets available for 8.75 euro/p (one way, off-peak hours only). From e.g. Rotterdam that's quite a reduction in train costs.

As for me, the driving will be still more convenient (except the driver itself) and cheaper than the public transport. It is around 70-90 minutes drive.

There are plenty of charging points in the Amsterdam and parking is free on weekend and after 18:00 outside of the Amsterdam Ring. And you can use public transport to get to any point of the Amsterdam.

You can also check parking spots in Amstelveen that is also easy reachable by public transport from Amsterdam.