You have to nip it in the bud right now. They are not allowed to sleep with you and that is final. You're the adults, what you say goes. The screaming and crying and whinning and begging is just to get you to do what they want. When it's bedtime everyone goes to their beds and that's final.
My 2 year old son asks me to sleep in his bed! I tell him I sleep with Daddy in my bedroom but, on the weekends I promise we can nap to together and we do. We take super long naps in my bed, it's great!
He cries loudly sometimes when I leave his room at night but, I assure him I love him and we'll make waffles in the morning. He stops crying after 2 minutes and is asleep after 5 minutes.
Stand your ground. It's unacceptable the kids are sleeping in your bed at night. They are running the house and in the long run it will hurt them. Babies can't make decisions and they don't really want to deep down.