Both my sister and I are stepmoms and I can tell you that what you are feeling is perfectly normal...as unpleasant as it is to admit it. HOWEVER, because we married into these situations with free will, it is our repsonsibility not to act on these feelings and to behave in an ethical manner. Our frustration is not the stepchild's fault. Our frustration is because we aren't getting what we want all the time and that we aren't in control.
As I see it, you have two choices. You can either let your stepson be your husband's sole responsibility and make him the primary caretaker for visits and whatnot. During the times he is with his son, you need to accept that just as he is serving as a "single" parent for that time, so are you.
The other option is to take on this child as a part of your entire family unit. That means taking responsibility for learning how to deal with sickness and 4-year old behavior as a given...just as you will when your babe is 4 years old. To make this work, you and your husband need to agree to work as a team with all things childcare, although I'd still let him be primary contact with the stepson's mom.
I think there are pros and cons to each set up. My sister does the former and I do the latter. My stepdaughter lives 20 hours away and I go with DH on the long drives for each visit. There are times that I resent the heck out of this (why can't they travel half way to see us, blah blah blah) but the fact is that I want her to feel like a part of this family and not just her father's daughter.
Hang in there. Get some counselling for the PPD! And decide which model you and your husband would like to follow. Then work as a team to make it happen.