Are we allowed to exit the museum to have lunch in the Tuilleries Garden and then allowed to re-enter? Or will security be an issue?
Security doesn't check tickets; you can enter the secure area without because many people are going to the book store or whatever. The only security line with ticket priority is at the pyramid and you would not use that again once having been checked through but use the Carrousel entrance instead without showing ticket. Once inside the tickets are checked at the doors to the wings and since often people leave to go to the cafeteria or for a short cut to another of the three wings, the ticket can be re-used and so you can come and go all day. I have done this many times. If it is not possible it would be a new thing.
If you leave the whole museum to eat (instead of going to one of the restaurants or food courts) you'll have to pass thru security again but it's not a big problem. You will go back to the Pyramid entrance and go in the ticket-holder/pass side so the line is not usually too long.
I love to eat in the Tuileries! The restaurants are a bit pricey but I love eating under the trees!
To be honest, I can get completely museum'd out in the Louvre. I always get the Paris Museum Pass so I break my visits up into 2-3 hours at a time so I don't get overloaded. Your schedule may not allow that, but if it does, please consider this strategy.
I seem to remember that your ticket is only good for only one entrance to any particular wing. That is, if you go into the Denon wing, you won't be able to get back into it using the same ticket. But you will be able to get into the Richelieu or Sully wing. This is to foil those n'er-do-wells who take tickets out of the trash outside of the museum, and try to re-sell them cheaply to uninformed tourists. This is only by my memory, so someone please correct me if I am wrong.
I have never had any problem coming and going from the wings; I am pretty sure I have re-entered wings, but am not certain -- the thing is you can get from one wing to another without going through the wing entrance -- it is just less convenient. I think I have just come and gone all day without issues -- but things change and it is certainly possible that enforcement might get stricter if there is abuse.
I agree with Janet, I've never had any problem going back and forth. I sometimes eat at the cafe that is on the Richelieu side so you have to leave Denon or Sully to get to it. No problem getting back in once you've revived with some food and drink.
Pam