Cotswolds in a few days!

Hi everyone, in a few days my wife and I will be coming to the Cotswolds, flying to/from Birmingham. We already rented the car and booked accomodations for the nights, but would love to hear your advice on what to see and and especially where to eat (my wife is lactose intolerant).

Here's the itinerary we planned from home, but it's open to changes:

  • Day 1 (March 7, landing at noon)
    • lunch just off the motorway in Knowle (we'll be starving lol)
    • Winchcombe (steam train station, Hailes Abbey, St Kenelm's Well, Sudeley Castle?)
    • Coln St Aldwyns
    • Bibury
    • Cirencester (please, tell us its must-see)
    • dinner ?
    • sleep near Stroud
  • Day 2 (March 8)
    • Stroud (for the Farmers's Market)
    • Minchinhampton
    • Tetbury
    • Castle combe
    • Lacock (Harry Potter Snape class)
    • Burford
    • Oxford (Harry Potter spots and anything else beautiful)
    • lunch and dinner ?
    • sleep just outside Oxford
  • Day 3 (March 9)
    • some more Oxford in the early morning
    • would love to find a Catholic Church to attend Sunday Mass
    • Chipping norton (does it make sense to have lunch at Jeremy Clarkson Diddly Squat Farm? I am a huge fan of him!)
    • Stow on the wold
    • Upper and Lower Slaughter
    • Burton on the water
    • Moreton in Marsh
    • Blockley
    • dinner ?
    • sleep in the area
  • Day 4 (March 10, plane leaving around 5pm)
    • Snowshill
    • Stanton
    • Broadway (and its Tower)
    • Chipping campden (with Broad Campden and/or Dover's Hill)
    • Honington
    • lunch on the way to the airport

We can't wait to be there and look forward to receiving your advice! Please, also tell us if you think it's too much to see in single days (and what would you take off the list). Also, do we need to pay attention where we drive/park (especially in the bigger towns such as Cirencester, Stroud and Oxford: we imagine there are limited traffic zones)? Thanks everyone!