Hi, and welcome.
I assume you'd need to rent the car: that would be a non-starter, sadly, due to the steep drop off charges if you rent in country A and drop off in country B. When I say steep, I mean well over $1,000.
And even if you have your car, the train is cheaper anyway, once you factor in petrol costs. If you go via Germany, you can have tickets for about 50 euros per person booked in advance via Deutsche Bahn. Possibly even 40. A random date in November gave me such €50 tickets. Suitcases aren't a problem as long as you can drag them along, and possibly up or down the odd stairs. It's a long train ride with 2-3 changes, but the drive is long too, and flying involves getting to Zürich, Geneva or Basel airports, none of which are very close to Neuchâtel...