As an instructor I do teach rudder even before solo but I do it up high, not at the time I'm about to teach landing. After what I went through myself I want a student to know what the rudder will do. Rudder takes time so I understand your problem and cross wind landing seems to be a big stumbling stone for new pilots. The time to learn is the same day you are able to do a figure 8 up high. Most of my students ask about rudder use so I have them climb then kick in some aileron and elevator then just a touch of rudder to see what the plane does. For those that don't have the rudder down so well I have them fly over to the windward side of the runway and allow the wind to drift them over to the center of the field and land. As long as the plane isn't weather vaining and just getting pushed I'm good with that. By this time they have aileron down pretty good. As an instructor I only go as fast as the student can progress.
How well does your instructor handle a cross wind?? Where I train now if the student can't handle the cross wind I have enough room to have him come in wide and land into the wind or close enough to it to make little difference. There ar a lot of ways to beat the wind but I would still have you shooting the approach up high just to teach you how controls work. A lot doesw depend on who isw teaching you. I teach landing with just the throttle, rudder and elevator. The only thing the ailerons are used for is to keep the plane level. Most of my students land much better then I do. No, I have no reason for this but it's true. I always took off better then my instructor??