Try Viamichelin.co/uk

They will give you alternate routes, show you any tolls, and the approximate cost for petrol. Get a diesel if you can, as it's cheaper than petrol in Europe.

Hope you can drive a stick.

That's an easy one. . I'd do it like that, you can skip the last part if you run out of time.
Fom unich Airport go west on A92 then A99 to A96. A96 to Munich/Garmisch, ot to Lindau. In Munich /Laim leave and turn right direction Garmisch, enter A95, go all the way to Garmisch. In Garmisch go ditrction Grainau cross the border to Leermos. Drive through Lermoos, when the road ends use 187, the Fernpass road to Imst. Navigate through all the roundabouts in Imst. Go south to Reschenpass, but I'd highly recommend a detour to Samnaun, CH. It's only a few km, but they've tax free status, so gas and booze is erlatively cheap up there. on 27 in Switzerland drive to Scuol and Sankt Moritz. On 29 to Tirano,IT from there to Bormio. SS38 take you to Stilfserjoch (Pd Stelvio). You'll be approching from the easier side, but going down will be very steep. Expect many bikers and cyclists. Don't kill anyone. You need to be a good driver. Go to 1st gear whenever needed. Then onward through the Vinschgau to Meran, south to Bozen, Gröden to Cortina.
If you're already fed up in Bozen, doing so much driving, you could also thake the autostrada from there. I've basically driven every road there is in the area several times. That's the bad thing about the mountains, there is only a limited number of roads through them. Reschen is easy driving. Stilfser Joch is dangerous mainly because if the many bikes and bicycles. Should you prefer driving up there from the Vinschgau, be extra careful, you will not be able to see oncoming traffic in some of the bends and some bikers have an imminent death wish. Be warned. And know how to use your hand brake to avoid rolling back after you had to stop.

Thanks for good help But where to sleep? We are planning this trip over two days (and two nights). Are there any nice hotels in the Alps? The last night we do not want to be far from Venice airport (max 2 hours driving).

2 days are very little time for the trip. If the Stilfser Joch is a must, you could skip St Moritz and Samnaun and drive from Lake Reschen / Vinschgau up the Stilfser Joch and turn at the summit an on to Bozen. Bormio will take more time. Or/and you can take the autostrada from Bozen to Venice.
otoh St Moritz has the finest hotels. It all depends what you consider a nice hotel. I stay at b&b's most of the time.
Try www.hrs.de

Okey, what about taking the first night in St moritz, an the second by the Garda lake?