Get there so you are in the park for opening. Make use of the fast pass system (free but tickets can run out quite early, they can also not). Have a look at the map off the website ahead of time so you know where you are heading for and if possible grab a parade and show schedule of the website. Also have a think whether you want to Just do the main park or the main park and the studios.
At a similar age my twos must sees were:
Café Mickey (So many fantastic pictures)
Main Park: All the shows and parardes, Thunder mountain ( not at two but at 5 my roller-coaster nuts were into it), Buzz Lightyear, Le Pays des Contes de Fées (out the back of fantasyland, usually closed but absolutely gorgeous very underrated little ride when open) Dumbos & Autopia Why oh why?!?!? small world and carousal.
Studios: Animagique, Stitch Live (We LOVE this) and the stunt show (we hide before the burning man stunt, Just after the hero falls/skids off his motorbike)
If your six year old isn't too into rollercoasters I would suggest the following to start: head straight for fantasy land and Peter Pans flight grab a fast pass, do fantasyland (inc Peter Pan at your fast pass time). Then head for Discoveryland and do it the same way, grab a fast pass for Buzz Lightyear intergalactic spin and do the rest. After this you'll probably be working round the afternoon parade schedule and you'll have seen enough to be able to say we're having an awesome day anything else is a bonus.
If you want to check out the studios park it can work quite well to do this after the afternoon parade (check the times for Animagique and the stunt show) as there are more sit and look shows for tired legs. Otherwise if you stay in the main park I would fast pass big thunder mountain (If your 6 year old fancies it), do Pirates of the Caribbean (a little on the scary side for your 2 year old), (miss phantom manor, which I love but scares the kids rigid) and anything else that was a favourite the first time round. If it's all getting a little overwhelming I would head to one of the walk-arounds Like Alice in wonderlands Labyrinth ( I disproportionately love this)(Fantasyland), or going up inside sleeping beauty's castle (this is a lovely last activity as you get to say bye to the park).
In general the fast food pizza joints are nicer than the other fast food joints. Colonel Hathis in Adventure Land has never let me down (always had lunch there before I went for the full board lunch plan last time) no wait before 12 a short wait after. At a fast food level the food is universally rubbish in the studios park, for one day I would say don't eat there!
I would avoid the meet and greets unless you are dead keen, the queues are excruciatingly long and utterly unavoidable whatever time you get there. Characters do a lot of walkabouts in the studios park, they have improved the mobbing of the Characters by the French guests who don't know how to queue but sometimes you do have to be a little pushy. Characters also sometimes appear in the uncover walkways either side of mainstreet in the main park.
Best souvenirs are always an autograph and their character friendly big thick pens (as soon as you hit the parks, in fact arrive early and grab one before you get in and bump into a character unexpectedly). Gives the kids a way of interacting with the characters, especially if they are a little timid and mine have really treasured them. Write your child's name clearly in the front of the book, I have once had a character write a personal message after checking out the name in the front. If you want a specific characters attention carrying a toy often works.