4 hours.

When is the last train from Kushiro back to Sapporo?

Leaving Kushiro at 19:08.

Is it possible to drive a car from Kushiro to Akan during winter or are the roads impassible?

It is possible. There is a small risk that the roads might be snow covered, but probably they will be free of snow.

Would you consider this a "day-trip"?

My wife and I enjoy skiing here in the U.S. and are advanced skiers, which ski resort should we go to?

Lake Shikotsu and Lake Toya are famous for a near hot spring from Sapporo.
Lake Toya is the place where summit was held in 2008.

http://www.laketoya.com/en/

If you want to play ski, Rustu and Niseko are very famous.

http://en.rusutsu.co.jp/winter/
http://www.niseko.ne.jp/en/index.html

So, I suggest that you make a reservation at a hotel in Lake Toya, and go to Rustu to ski.
There is also a bus which turns on Rustu from Lake Toya.

I want you to see URL and to refer to it.

I stayed in Kushiro for two nights so that I had enough time to explore. Kushiro has a list of good hotels. One of them is the brand new Route Inn just opposite the train station. Another nearly hotel is Tokyu Inn, quite a decent one as well.

I took a tour bus from Kushiro to Lake Akan(Akanko). The tour stops at five different attractions before reaching Akanko. Lake Mashu is breathtaking. The bus only stops there for about half an hour for pictures. Tsurumidai, a feeding ground for the Japanese crane is really something with all those majestic birds flying and playing right in front. Next is Logan, a sulfur mountain. Akanko is deeply frozen. The stop is about one and half hours. Enough time to hire a snowmobile and do some fishing in the frozen lake though. There are only one tour per day on Saturday and Sunday during the winter season.

Direst scheduled bus services from Kushiro to Lake Mashu are quite rare. Most buses go either to Lake Akan or Lake Kawayu, another bigger lake in the park. Late Mashu is just a transit point with a short pause. I think there are about 4 to 5 daily bus serives to these places. The bus stop is located in front of the train station.

The roads are passable despite heavy snowfall in the park.

The tour ticket is sold at the lobby of the Sakura Hotel next to the train station. No reservation is required.
The bus stop is just outside the hotel. This is a commuter bus stop shared by many other buses as well.
I think the bus leaves at around 8.30am. It is a whole day trip. Lunch is not provided.