We love Italy and have been many times, but last year was our first stay on lake Garda. We are returning this summer.!!!!. The route you propose is a popular one and should not cause problems for any well matched outfit. We have crossed Switzerland via the St. Gotthard and been held up more times than not. Other people we have spoken to have not been delayed. We now prefer the German route, entering Italy via Innsbruck. You need to be aware that it will take 3 steady days towing from Calais or 2 big ones of 400 miles each. However, Garda is beautiful and I am sure you will enjoy it. We stay at Fornella but there are many sites to choose from.
Happy travels. BarryB