I am having a huge amount of trouble trying to dock large craft (like the tugs that Newman's Eve lander used to get to Eve). Has anyone got any advice?
Actually, those tugs aren't even close to the largest stuff I dock to one another, and are fairly easy to dock. Without getting into discussions on whether mods are cheating or not (which basically depends on the mod, anyway), I will say that I don't use any mods in my craft designs and also don't use mechjeb, and I dock them just fine. While that laser mod might help, if you're having trouble docking mid-sized ships that suggests you're doing something wrong. While a mod might help you get around the things you're doing wrong, addressing those issues is always the better approach whether you end up using mods or not.
So let's get down to business. There are two major things that are important with docking; craft design and RCS maneuvering.
1) Craft design: half of your successful docking maneuver is done before you ever leave the ground, in the VAB (or SPH, depending on the craft). Efficient RCS setup is the key to controlling your ship efficiently once in orbit; those tugs of mine had a large monopropellant tank each, but that wasn't because they needed that much to dock to the Defiant (Eve lander) - 750 monopropellant is easily enough to handle a dozen dockings. It was rather because the Defiant was a pretty special case that needed to be able to keep it's nose straight up during the first few seconds of launch from Eve surface; in case it landed on a slope it needed lots of powerful RCS thrusters to quickly set it straight. This also meant that the Defiant was a fuel guzzler when it came to RCS fuel, hence the large tanks.
The tugs themselves were easy as dirt to dock. Neither of them used quad thrusters, and I would suggest not using them on craft that don't absolutely need quads for some reason - and those you'll just dock around in orbit don't. Use linear thrusters instead, and try to position them at equal distances from the center of mass. So basically, 4x symmetry side linear ports near the top and bottom on each side of the center of mass; these will provide sideways thrust. You'll also need to be able to thrust forwards and backwards, so put another 4 backwards oriented ones in the back, and 4 forward oriented ones in the nose. Give them a large RCS tank and with a little practice you can dock anything many times on a single large tank. Or save some weight and give them smaller tanks if you feel you won't need that much and are confident of your abilities. Either way, efficient RCS setup wins half the battle before it begins.
While on the subject, I'd also like to address the myth that RCS + ASAS is a bad combination. Indeed it can be, either on rather large ships, or on ships with a badly designed RCS setup. See, well placed RCS thrusters won't create much torque when you just want your ship to go sideways; if they do, ASAS will try to compensate by periodically firing thrusters on the other side to countermand the rotation produced by the pair you activated. Introduce some wobble and shaking of the ship and you got ASAS spraying your RCS fuel all over the place. But the solution to this problem isn't always to not use ASAS, but rather to make the ship not wobble / turn when you activate side thrusters. Design your RCS system well, and ASAS-induced RCS mess will be kept to a manageable minimum at worst, or won't be present at all at best.
2) RCS maneuvering.
This won't be that much of a problem if you've designed your RCS system properly. Remember to use the navball's information to your advantage. You have speed relative to target and vector relative to target, those two tools give you a lot to work with already, allowing you to kill relative velocity to your target by finding the retrogade icon on the navball (while in "target" mode), and burning prograde in it's direction. Melt your speed difference to your target to 0.0 and you'll seem to stop (again, relative to target) - it's a good idea to do this some 100m or so away from your target. Then take a moment to plan the final docking approach - select the docking port on your target you want to dock with, right click it and set it as target. This can be helpful with your navball, as your target indicators now point to that docking port and not the target's command module. Now take your time, and slowly position yourself so your nose is oriented and lined up to that docking port. Slow and steady wins the race here - go too fast and you'll spend up twice as much time lining up as you would have if you were patient. Use different camera views to line up your craft as best you can. Once done, lock your orientation with ASAS, give yourself a bit of forward motion towards the target (0.1 or 0.2 m/s is fine at this point) - this is just so your prograde vector appears in front of you. Now you can use the side thrusters to line up your nose with the pink target indicator on the navball (the pink target with a circle). If you have your nose, the pink target, and the yellow prograde icon all at the same place on the navball, it means your nose is heading straight for the docking port. This is good, assuming the docking port is actually in your nose - if not, adapt the method to the side of the craft the docking port is at
Whew, a lot of text. Hope that helped some.