how bad is the drive from Disney Paris to Versailles in July? Sunday vs. Tues?

The drive in itself is not so bad, traffic jams can make it bad.

I have done this in June 2013 on a Wednesday morning, so a weekday and I needed about one hour via the A86, there was hardly any delay. But for the opposite direction during rush hour on a Tuesday last June I needed if I remember well some 3 hours. Traffic jams/slow moving traffic till the exit to DLP on the A4. Going to Versailles during the day will be not so much of a problem, but expect the Parisians will come back in the evening from their weekend trip, traffic jams will at least worse as rush hour during the week. It also depends if somewhere happens an accident, so it remains hard to predict how much time you really will need.

The French go usually on holiday in August, so think July and June are comparable.

Tuesday definitely preferable to Sunday in July.

(And as Will pointed out, long train with connections could be preferable to three hours in a traffic jam, by which time you could have already made the journey by train.)

Is there a reason why changing from one train to another is a particular problem for you?

It is only 2 simple changes, at Chatelet Les Halles and St Michel. 89 minutes, no hunting for parking, no traffic jams....