It sounds like your DH and I can be kitchen buddies. Has he ever tried cooking them in a pressure cooker? They take about a 1/3 of the cooking time then.
I take it you mean their different tomato sauces? In the States most of the Mexican foods are really Tex-Mex. Generally any Mexican foods with cheese in it is Tex-Mex and based on northern Mexican recipes.
The green ones based on green tomatoes or and tomatillos (something which is unrelated to the tomato) and red tomatoes.
I make my sauces (based on Southern Mexican - Yucatec cooking) Where they put serrano chilis, I put very finely chopped habanero peppers and would add lime juice too to taste.
Recipe for salsa verde (substitute red tomatoes for a red salsa. Tinned toms work just fine.)
500 grs. green tomatoes
½ onion
8 serrano chiles (not very hot)
2 sprigs cilantro
1 clove garlic
Salt
Method
Put in a frying pan quartered tomatoes, oil, roast them with serrano chilies, garlic and onion. At the time they are a bit toasted, put them in a blender and added salt and cilantro.
If the blending, is too thick and difficult to liquid, you can add a little water, but very little.
There are variations of the green sauce consisting of avocado and pistachio instead of cilantro for example. There is a Yucatec one with toasted pumpkin seeds too. These are great for vegetarian/vegan diets.