A limo is a fun and stress free way to go wine tasting. I have never heard of a winery having a problem with a small limo with 4 passengers. Some wineries do not allow the big party limos usually full of passengers who have had way to much to drink.
The weekends are very crowded. Maybe do your wine tasting in Napa Valley on Thursday and Friday and head up to the Alexander Valley on Saturday. A beautiful drive and relatively not very crowded.
I have always enjoyed having a glass of wine on the deck at Auberge du Soleil in the late afternoon.