This may not be realistic, but here's a potential solution.
Step 1: Stay and play with them at the childcare. Keep this up until they are happy and engaged.
Step 2: Remain in the room and read an adult book to yourself. Ignore them. If they come to you, assure them that you are here and they need to go play. You are busy. If they need help, they need to talk to the teacher. Keep this up until they are comfortably ignoring you.
Step 3: Tell them that you will be in the building, and go into a back room. Hang out with your book. They know you're there, but they can't see you, hear you, or interact with you. Keep this up until they let you go to the back room without a fuss.
Step 4: Let them know that you will be going out for a little while to do boring things. Ask them to have lots of fun for you while you're gone. Make your first outing short. Extend until you're up to the full amount of time you want childcare.
Work hard to make this better, but listen to your children. Not every child is match for every childcare. My son had a awful time at his first preschool. They weren't bad, just not a good match for him. It was 2 days a week of preschool and 5 days a week of him talking about how much he hated it. After six months of trying to make it work, things were worse than ever for him. We pulled him out. A year later, we tried him in a different program. He loved it.
Good luck!