I was a Nursery leader, but I have no great advice for you. Can you talk through things with them? Could you take them to Nursery and say, "Mommy's going to go outside the door for 2 minutes, and then she'll come back." Do that a few times and see if it helps. They usually freak out because they aren't sure that you'll be coming back.
Make absolutely sure that they can't see you through the window, too, while you're outside. My MIL is the Nursery Leader and she said you'd be surprised how many parents peek through and assume the kids don't look up and see them.
Could you try staying in Nursery with them, but gradually start moving away from them? If they want something (like more snacks), have them ask the leaders for it. That could help them know what to do when you're not there, and to trust the leaders more. Kids know who takes care of them, so let the leaders do some of that and see if that helps.
I'm so sorry. I worried that my boys would be like that, but I have the opposite problem. My 2 year old takes off from Sacrament Meeting and speeds down the hall to Nursery ahead of me. He could care less if I dropped off the face of the Earth because Nursery is so fun. And it's hard to get him to leave when church is over.