We've been to Disneyland Paris twice, so I can help with a few things (not Davy Crocketts though as we've not stayed there, only the Sequoia Lodge and Newport Bay).
Driving there is so easy, we went by Eurostar the first time when our youngest child didn't need a train ticket but now she's over 4 years old the cost of 2 adults and 3 children on the Eurostar plus train from Sheffield and a night in London either side of the trip (requiring two hotel rooms because we're not a 'standard' 2 child family 🙄) is just sky high! We got the Eurotunnel 'free' by using Tesco Clubcard vouchers - £50 of Clubcard vouchers turned into £150 to spend on the Eurotunnel. So it's worth saving your vouchers for that if you shop at Tesco. There is a toll to pay each way on the French motorway (currently €21.70 I think, you can pay by card or cash and the machines give change). There are lots of hotels near the English entrance to the channel tunnel but what we did (again for cheapness since we need two rooms) was drive down and go through the tunnel all in one day and then stay overnight in Calais. It was this hotel we used, it was really easy to find both when getting off the Eurotunnel train and when coming back from Disney (we stayed there both on the way to Disney and on the way home. It's definitely worth staying in Calais on the way home then you are not clockwatching on your last day and thinking about having to leave by a certain time to get your train) m.accorhotels.com/gb/hotel-3300-ibis-calais-tunnel-sous-la-manche/index.shtml. Having done the drive once we said that next time we'd actually drive for an hour or so once we got off the Eurotunnel and then we'd be a bit closer to Disney for the drive the next morning. We left Calais at 08:15 and arrived at Disney just before 12, that was with a 30 minute stop, so it's about a 3 hour drive from Calais to Disney. There is an Ibis hotel at a service station about half way between Calais and Disney, I think I will look at that one for the journey there next year but still stay in Calais on the way home.
We found these driving instructions very useful janey901.blogspot.co.uk/?m=1 It's a very easy drive, I was quite suprised to find the French motorways a LOT more civilised than the uk ones! I guess driving time from Manchester will be similar to our time from Sheffield, it was very manageable and I wouldn't do it any other way now.
I filled our car up with diesel at a Tesco filling station a couple of junctions on the M20 before the Eurotunnel terminal (I think it was Tesco Extra Ashford Crooksfoot), it was 'normal' prices and I knew we could get to Disney and back from there on a full tank so that eliminated the worry of working out the French fuel pumps and remember what diesel is called there! We only used a tank and a half at most for the whole journey, I reckon it cost about £110 in total (I think our car does about 60 miles per gallon, perhaps more when it's all motorway driving).
As far as I know you can take any food you like with you, the Eurotunnel website would have a list of things you can't take I guess. They probably do random spot checks, but our car boot was never opened or searched.
We've only been to Disney for February half term (ours is usually the week after most of the rest of England so it's been the last week of February that we've been both times - 2014 and again this year), so the parks haven't been packed, but with 4 nights there you'll definitely have time to do everything you want to in both parks. Even more so as they will be open later in the summer, they closed at 8:30 in February. You will be able to get into the Disney park (as opposed to the Studios park) from 8am since you are staying at a Disney hotel, but it depends how tired you all are as to what time you wake up in the morning! I don't think it's worth dragging tired children out of bed military-style, not all of the rides are open between 8-10am anyway, it's mostly the 'tamer' rides not the rollercoasters. The Studios generally open at 10am, it's worth getting there from 9:15 onwards to queue at the gates as they do open before 10am and you might want to do a mad dash to ride Crush's Coaster or Ratatouille one morning. The queues do tend to go down around the time that the parade is on (17:30, although it may be slightly later in the summer, you can always check nearer the time) and stay a bit shorter as people start to have their evening meals.
Buffalo Bills is good, I'm not sure I'd say MUST do as it's a bit expensive, but our children (DS 11, DD1 8 and DD2 4 at the time, she's just been 5 this month) really enjoyed it. Don't go for Category 1 seating, the arena is not massive - we were as far back and as far up in the Category 2 seats as you could get and we still felt part of the action and had good views.
Must-do big rides (depending on whether or not your children like big rides!) are Rock n Rollercoaster, Tower of Terror, RC Racer and Crush's Coaster in the Studios and Indiana Jones and Big Thunder Mountain in the Disney park. There is also Space Mountain in the Disney park - recently re-branded to have a Star Wars name that I can't remember exactly - but I don't like that as it really rattles your head around. Of the tamer rides Peter Pan is magical, you have to go on It's a Small World and the carousel too! I wouldn't bother with Phantom Manor (it's a bit boring), oh and I forgot there is Pirates of the Caribbean too, that was closed when we were there this year but is worth going on.
This website is very good for planning www.dlpguide.com and nearer the time will have park schedules and parade times on it plus the park closing times (you could have a look at August for this year, I expect it will be the same times for next year). You must stay late for the laser light show and fireworks that are on in the Disney park at closing time, it's just changed for the 25th Anniversary this year and is called Disney Illuminations.
Hope some of that essay helps 