My toddlers are by my side 24/7

I have a almost 3 year old and one year old, they are always by my side.. it’s kind of suffocating but when they are not I get nervous, we recently got our own place with our own rooms but they are scared to sleep alone, they cry for me all night til I grab them.. so I’ve ordered stuff online like bed rails crib bumpers night lights and stuffers for their rooms, which are just right across from my room, my baby sleeps on his bed right beside my bed and my baby sleeps in my bed by me.. how can I get them to start sleeping alone in their rooms? And how can I get over my anxiety if sleeping alone in my own room too? Lol I guess it’s the separation for all three of us because we left their abusive father a year ago, so I always get scared something will happen if we’re all sleeping in different rooms.. also the rooms are upstairs but I have a baby gate blocking the stairs so would I leave the room doors open? Including mine?