Venice to Vienna could be done by overnight train - save travel time and the cost of a hotel - but that stretch of track in Austria at least is very scenic.

Going by train to Prag and Vienna is really easy and its cheap, especially if you buy in Germany, with the Deutsche Bahn.>

that would be www.bahn.de/en for fares and schedules and to book discounted tickets as low as 29 euros flat fare for any direct train trip - but those discounted tickets have severe restrictions regards changes (none allowed) and refunds (15 euro cancellation fee) and may sell out early so must be booked, kind of in stone, weeks in advance to get but can save a ton, if you don't have a railpass,over just showing up and buying at the stations.

Concur with Spaarne--you don't have time to do both Italy and central Europe.

If you stay in central Europe, you could also visit Salzburg, Hallstadt, and other neat places in Austria, and perhaps the Tyrol (Innsbruck).

Many thanks for all your help and advice . I know it will be very short time in each place , but my mom is coming from far away and she feels might be the last time she can come and make such a long trip , so we are definitely trying to show her what she wants to see the most .
I know have a clear idea of how to get there and my best options! Thanks again!!

*now