Boy oh boy! This is a difficult and heart-wrenching problem!
My question would be what is scaring her? Is she afraid you will leave forever? Has she had bad nightmares? Try to figure out why she is behaving this way. This is obviously not normal. My son had terrible nightmares, and would have terrifying visions throughout the day. He was constantly terrorized. Thank God, they stopped when we became Orthodox Christians.
Maybe she is being bratty, but I doubt it. I have a little one who loves to cuddle a lot, but I'm not experiencing that she is afraid of anything. I get the sense that your daughter is afraid of something. Once you know, you can talk to a counselor, a priest, a pastor - someone who can help settle her down.
Sometimes when my children get really anxious, I try to calm myself as much as I can. Then in a calm state I have them look into my eyes, and I hold them, and say , calm down, relax - I'll give them some massage on their backs. I also show them calming pictures. If they have a fear about something, we'll talk about it. I don't know how verbal your daughter is. It can be difficult to draw a almost 2-year old into talking accurately about something, but maybe she can tell you what's bothering her.
If her verbal skills aren't good, there are sign language kits you can buy to help your children express themselves better until they can really talk.
I agree with the other parents, that this child can't constantly be dominating your time either - the other child is not getting her time. I hope and pray that you will come to a quick solution. God bless!