Hmmm... strange that someone who mastered Red Front shouldn't be able to master 2nd Front (from my point of view at least, I thought RF was way harder!)
It's been a while since I played, but I don't remember D-Day being too much of a problem (once you know the right cities to attack with combat engineers
). On your first turn start moving your paratroopers into position to take St. Mere - if you move them into the correct positions its possible not to lose a single one on the German counterattack. I usually use the commandos to block the road from Caen to the cities on the coast. Make your gliders land within range of the naval battery near Ouiestraham - it will waste all of its shells attacking your gliders, leaving you with only the mines to worry about on your approach to that beach.
Make use of the Crocodiles 'all as road' ability to assault the cities on the British beaches (except for Arromanches, Ouiestraham and the 2 naval battery cities - use combat engineers for these). Then send in commandos (all as road) to seize them. You can also shell them with your battleships or bomb them to further soften them up, although I prefer to use planes to attack stacked troops or tanks out in the open. This also has the bonus of blocking enemy movement. If you want some more planes, try in the top right and left hand corners of the screen for German fighters to shoot down ( I think Xin Yu discovered this).
An essential piece of information when bringing your LCVP's closer to shore - if they're carrying tanks, the computer will shell them. If they only contain troops, the computer will not shell them. You still have to watch out for the mines though.