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.