My suggestion is to try and reframe how you're thinking about this... if you were married (you don't say whether you are), would you want your husband to help you with the tasks of raising your child? If you and the father were together, would you expect that, as a married couple, you would share the burdedn of child-rearing tasks? What if you worked full-time during the hours when most doctors offices are open - would you enlist the help of your spouse to get the child to and from the doctor/dentist/school/etc?
Most people answer yes to these questions. Where it gets muddy is when steps are involved, and then it becomes a "territory" issue, more than anything else. My suggestion is to focus on the child. If your son is getting the care he needs while he's with his dad, does it really matter if it's dad doing the driving or mom? Or does it matter that he's getting what he needs? In my view, it matters that he's getting what he needs.
I know it's hard to deal with another "mother figure" in your sons life. But don't forget that your son is capable of loving all the people in his life - he doesn't have to choose between you and his step-mom. He has enough love in his heart to love you both. And, especially having special needs - he needs all the love he can get. If another person has come into his life that loves him, and is willing to make sure that he is well loved and cared for when you're not physically there - I personally think that's something to be thankful for, not something to resent. It doesn't make you less of a mother if she takes him to doctors appointments.
As far as you being the "legal guardian"... you state that you have joint legal and
joint physical, and you have a 50/50 parenting schedule (according to another post you made). That means you are
both legal guardians. As such, you can designate another person to act in your stead when it comes to these things during your parenting time, and so can he.