driving switzerland in november

Yes you will have problems. In the lowlands you will be OK, but most of the high passes over the Alps are closed by snow from November to May. Even if the passes are not yet closed in the first week in November, you will encounter snow and may need snow chains.
For 6 months of the year, the only way to get by from from one side of the Alps to the other is by rail or road tunnel. And the only way to get by road from one half of Switzerland to the other is by one of two long road tunnels, the Gotthard Road Tunnel or the San Bernardino Tunnel.
Road maps mark the dates passes are usually close each year, for example "11-5" means closed from November to May.

Can we go by train from Munich to Milan with some overnight stops in Switzerland (area close to Lichtenstein)?

f4439328,
Were you planning to drive with a hire car from Munich to Milan?
A one way car hire from one country to another usually has a large surcharge. There is nothing to stop you driving to Milan and then back to Germany, but returning a German car in Italy will be very expensive. You need to check the full cost if you are planning this.
I think I may have been over-negative in my last post. Driving from Germany by Italy using the Autobahn (Motorway) and through the Gotthard Road Tunnel is no problem. But getting off the Autobahn and going on side roads or further up the valleys will be difficult.

Yes, you can go by train from Munich to Milan. The shortest route would be Munich - Zürich - Gotthard Rail Tunnel - Lugano - Milan. You need to first decide where you want to stop off in Switzerland, then you can look up train times on www.bahn.de (German Railways website) or www.sbb.ch (Swiss Railways).
Click here for a rail map of Switzerland, which may help in your planning: https://www.swisspasses.com/railpass/overviewmap_en.pdf

There is not much to see in Liechtenstein.

Sounds like a lot more travel research is in order. Switzerland is for trains.