night terrors are an aweful thing to have to deal with. they do NOT have anything to do with tempers, or wanting to sleep with you. she isnt even aware that she is having them, and couldnt tell you what or why she was having one.
i used to have them when i was a kid, and surprisingly in 25 years what they know about them have not changed. first of all, she will grow out of it. second, they dont know what causes them or why some kids have them and some kids dont. thirdly, the only advice they give to parents is to NOT try to wake the child, just make sure that they are safe and not able to get hurt. you can comfort them, even knowing that its not going to make them stop any sooner - i think it mostly does help your sanity to know you are there trying to comfort them. there are cases where a kid will wake up in a night terror and be confused, so at least you can be there to lay them back down and that its ok.
ok, now on to issue number one, the sleeping issue.
as kids grow, they often take 2 steps forward and one step back. how you deal with the one step back determines how your child takes the next 2 steps forward. i believe as parents we need to do our best to nuture that step back. do what you need to do to get sleep, even if it means that she isnt in her own bed. however, that doesnt mean she has to be in your bed.
maybe you could try to take the matress off her bed and put it on the floor in your room. gradually you should be able to move it out of the room and back to her room. 2 is a young age to really expect her to want to be so far away from you all night long. its scary for a child to wake up and not have mom or dad near. the more sensitive you can be to your daughter during this time, the more confidentally she will be able to move forward. kids, contrary to popular belief, are not born with self soothing, are not born wanting to be independent, and healthy dependence is how to develop independence. independence that comes out of forced independence isnt really independence. thats where you have the kid clinging to moms legs all the time... they are scared to be independent cuz they havent had any healthy dependence. your daughter at 2 definatly still needs healthy dependence.
dont forget that our kids grow up too quickly as it is... dont feel like in order for your kid to grow up and independent that you have to push her away, especially now when shes so young.
i see you have 4 month old girlS so i realize that this is probably a LOT of work. i cant relate unfortunatly. but i still think that maybe shes feeling a little lonely and worried if you still love her as much as the babies. this could very well be kinda a jealousy issue. i dont know if you are doing anything like this, but maybe once a day do something that is just for you and your older daughter to do together. take her out for ice cream, or lunch, or just a picnic in the backyard while the babies are sleeping (or better yet, with a babysitter or other family member)
try it out and see if that one on one time helps.
anyway.
hope you are able to work something out for her. sleep is hard and its hard with more kids.... so good luck