Welcome to Fodors (to train is like a lot of verbs to car, to bus, to plane, they don't exist )

I wouldn't shorten my time in Oxford to rush to the Cotswalds and then rush past Oxford to get to York. If you end up with a car in York it will prove of little use unless you want to go out and visit the countryside.

If you want to look at local transport for areas near York use http://www.transportdirect.info/Web2/Home.aspx?&repeatingloop=Y to get an idea of times. There are some very fine ruins in Yorkshire but you could also catch the train into Leeds.

As it is, you haven't much time for Oxford. And it takes time and trouble to pick up a rental car, figure out your way around, drop the car at your destination and get to your hotel. Not to speak of driving on the other side if it's not what you're used to.

So I guess it's a matter of priorities. The English countryside in the spring is a beautiful place to tootle around in a car. But I don't think that fits into the rest of your itinerary.

The train from Oxford to York goes through OK, but not terribly interesting scenery: much of it is interesting only for the back door view you get of English de-industrialisation.

The argument for going into the Cotswolds (which rather takes you out of your way) is that it gives you a chance to be part of very pretty countryside which your outlined journey seems not to expose you to if it's by train - though I'm not at all clear how you all plan to get yourselves and luggage from London to Windsor to Oxford in the same day. Are you?

But it represents a fair bit of driving. The quickest route (Oxford-Burford/Stow/etc then M40, M42 north, A42, M1, A1(M), A64) represents a good 6-7 hours behind the wheel, before comfort or sightseeing stops. That's over twice as long as the direct train will take, even apart from the faffing about with getting to the hire place etc

Only you know why you're thinking of your Cotswold day. If you just want exposure to countryside, Oxford is unusual among cities anywhere for how deeply the countryside penetrates into the middle of the city. From the railway station along the canal north, from Christ Church (the physically largest college) along the river east and west, and inside Magdalen College, rural footpaths take you through proper countryside, which you hit within a few minutes. The paths from the station and Christ Church would lead on for hundreds of miles to the coasts or the source of the Thames
if you had a few weeks to follow them.

The riverside path along the Ouse in the middle of York pulls a similar, but less spectacular, trick, and Arthur's Seat in Edinburgh is probably the wildest bit of nature inside any British city. A few hours' proper walking in any of these three will expose you to at least as much rurality as driving through the Cotswolds.

No thatched cottages, though (but you'd have to divert a bit from Burford to get to the first bit of thatch)