I'm new to this board but I am 28 & have been a step mother for 5 1/2 years now so I feel like I can have some insight into your situation.
First a couple of questions? Has the custody arrangment been finalized and filed with the court? If not, you REALLY have to get one. It just makes everything simplier and that way there is no confusion on who gets what time, etc. Your dh's ex sounds like mine, who would take visitation away when she got mad. I LOVE having an agreement to fall back on and quote, etc.
You Have to Have a Formal Agreement. It might cost you $$ but it is money that is well spent for your sanity.
That being said, she should be sharing the pick up, drop duties. I think it is important for the kids for their parents to interact on some level at both houses, even if it is just for drop, off, pick up, etc. This duty should be completely 50/50. Also it allows forces her to see you, even if it is only occasionally, and you can always be sure to have a kind word.
However, have you talked to your fiance about how you are not comfortable with him making the drop off decision without you? Ask him for a compromise. You would like to go, but would be willing to wait in the car. This way you can interact with the kids, help get them in the car, etc. Also, every once in a while, you can get out, smile and wave hello. (This can be on the pretext of helping with the kids) It might seem small but it all adds up.
I hear you on the baby sitting stuff. I could watch my ss full time, but he still did after school and daycare, because his mother wasn't comfortable with me having too much time with him. You just have to let that go. She feels threatend and it can be hard for her to realize that you could never replace her in their heart. Hey, if you try, you'll only upset the kids.
We do sporting stuff with her and that helped. Her finally finding someone helpsed, but she can still get crazy. One thing that really helped was setting up an email account for all our out of town family for my dss. Sometimes we'll have him e-mail her. That has really seemed to calm her down for some reasons.
Just keep doing really small things, and don't worry about the rest. Talk to his family once, make sure your df supports your need for his family to support you!! Then just deal with them as best you can. If your df, had a court agreement then she wouldn't have any say about them seeing the kids, because that would be all up to you and your df. It is neccesary for everyones sanity.