The Dothraki Sea doesn’t really have strategic points or river crossings, that’s kind of the point.
I’d say what you need is:
- Combined arms with disciplined infantry and cavalry. Archers and pikemen working together could hold off the lancers and the screamers while trading evenly with the horse archers, especially if you can train them to form square (multiple squares that can mutually support and pour fire on the Dothraki from the flanks and rear is a good idea). Put some good heavy cavalry in the center and use them to counter-charge vs. screamers and lancers, make sure to train them to regroup rather than pursue (keep them near the squares at all time), and whenever possible to wheel and charge the Dothraki towards a square to catch them on the pikes and prevent feigned retreats.
- Mobile fortifications. I would use a combination of the corral method used by the Boers and the Roman fort-building, together with the liberal use of entrenching tools to construct ditches and berms to reshape the battlefield. The Dothraki thrive on being able to attack on horse from any direction – with mobile fortifications, you can deny areas of the battlefield to them and make yourself much harder to attack from horseback. A dismounted Dothraki is much easier to kill.
- Lots of supplies and firepower. The real danger is that you beat a handful of khalasars, but run out of food/water or arrows halfway across the plain and then you get swarmed and die. So you want to bring a lot of supplies in your caravan – again, using corral techniques to protect your wagons.
- Utter ruthlessness. This is the part that really troubles me. Because if you were going to take the Dothraki Sea, you’re going to have to do some very ugly things. Murder their herds of horses, set grassfires from behind firebreaks etc. But the worst is the deliberate destruction of Vaes Dothrak to destroy their morale and sense of manifest destiny.