I think it might be a good idea to get your girl a checkup just to be sure there is nothing physically wrong. Then maybe go see a family therapist, and describe what is going on. The therapist could give you suggestions about what is going on with the child and what is going on with you, like, where you draw the line and how to modify your responses so the baby does not get trained to expect you to continuously respond. I don't know what those idea would be, or I'd give them here. Since you have a 2-year-old, you obviously know that this stage does not last, so if you say it is extreme, I assume you know what "extreme" is. I'm sorry I have no answers, but I think you need some help, and a good counselor can give that. Ask your ob-gyn for a referral.
Let her cry it out.it will be hard. I know. I had to do it with my son. There was a month where if i took just one step away drop him he'd start bawling like someone was beating him. I just had to let him cry it out. Go somewhere she cannot reach you. And let her cry. Of corset make sure she's completely safe or there another adult around. t either that or ride it out. Which can last for years.
It will eventually work. You have to stick to it. You have to be stern with it and most importantly you cannot give in.
I have a 9 month old that would sleep for about 5-6 hrs then wake every hour and a half after (this was at about 6 months) I would do bedtime routine bath then book and bottle and would put him to sleep in his crib. If (or really WHEN) he woke up after that first chunk of time I would bring him to bed with me and hubby and give him a bottle. Then he would wake every hour or hour and a half and I would have to feed him a 4-6 oz bottle each time he woke for him to fall back asleep. This is when I started getting concerned and so sleep deprived so I said I have to do something. I know he isn't hungry he needs the bottle to soothe himself so here's what I did. First I stopped bringing him to my bed. Second and very important- I timed him. Not just look at the time on the clock and decide to go in after so many minutes but I set a timer on my phone for 10 minutes. The amount of time is up to u but this was perfect for me and baby. So 10minutes on my phone if he kept crying and it got to "that level" I would go in check on him even pick him up. As soon as he was calm and his breathing was even asleep or awake I would put him back down and say goodnight. If he cried again I would set my timer and repeat. He always cried again at first but it only ever took a couple times before he was fast asleep. And then it would get to where he would never last the ten minutes before falling asleep without me having to go in at all. Now at 9 months he's always asleep by 8 at the latest which is also crucial, and wakes up around 7- 7:30. He does wake up around 4am for one 6 oz bottle which is the last one im trying to get rid of but this one is a little tougher lol and its an easy give and go and hes back to sleep so when he's ready we'll work on it which would be my last tip. If baby has anxiety from separation slowly ease yourself further and further away until your out of the room completely woth no tears :)
Wow sorry I wrote so much! My fingers were flying my goodness didn't mean to write a novel! ^.^
I had a similar situation with one of my 7 month old twins. She was definitely a mama's girl. I tried letting her cry it out but that absolutely broke my heart. So, I refused to pick her up. When she started whining and crying, I would go over to her and give her a toy and then continue doing something else in the room. Then, when she started again, I would pick her up, kiss her, and then set her back down with another toy....and back away continue doing something else. I kept repeating this and telling her that she was alright and now, she is able to understand that mommy is there for her but that she can comfort herself with a toy, pacifier, etc.
I don't know if this will work for you but good luck! :)