I'd agree to visit it before-hand as well if this is an important sight for you. The Palace is closed on Mondays altho the gardens are open. (editing to add - Jane beat me to the punch on this information!)
I'm not sure how your days fall but I'm suspecting your Sunday is the first Sunday of the month? During winter months the 1st Sunday is free entry but by May that does not apply. I thought that the fountains were turned on on the first Sunday of the month but I looked quickly thru the website and don't see that information.
I'd probably get a 2-day Museum Pass for Sunday and Monday and then you'll get another 2-day one on your tour. Are you staying at Hotel l'Empereur? If so, there are 2 easy places to get your pass. One is at the ticket office at Les Invalides right across the way from that hotel and the other is at a tabac (tobacco shop) right around the corner. I'd not bother to order one ahead of time. They are very easy to get in Paris as long as you don't try to pick it up at one of the very busy sights.
As to Versailles, I have been and it's good if it's what you want to see. The Palace is always jammed and there are pickpockets working the rooms. In fact, I went there on the Best of Paris tour, so we had a guide who was talking to us thru the whisper listening devices. At one point one of the guards in one of the rooms signaled her and she went over to talk to him, then told us the guard said there were pickpockets in the room. Anyway, I love the gardens, the Hameau and the Trianons. I wound up spending the whole day there. Literally - got there with the group just before opening and finally got on the train to come back to Paris at about 6P. I was not finished seeing things but I had run out of steam, lol!!