Well you and your husband certainly have your hands full. I am no expert but it sounds to me like ever since your second child came along, your first daughter went from being the baby and having all your attention, to now having to take the backseat to her little sister. She clearly has resentment toward her sister and you eventhough she doesn't realize it and can not express it verbally. I think it is extremely important that you spend a little bit of one on one time with her once in a while. Have a special day with just her and you and allow your husband to have a special day with him and your younger daughter and then the next time swap. It doesn't even have to be a whole day. Each of you take one child for a couple hours and do something special together so your oldest and your youngest will each know they are special and they won't have to compete for your attention during your special time.
Also, I think it's important not to use it as a reward for behavior, but choose what the activiy is as a reward for good behavior. In other words, you and your four yr old could get your nails done together when she is really well behaved for a week or two, but if she throws the cat or is acting out violently then when you have your special time, just do a picnic.
Another suggestion is at the end of the day or couple of hours, the four of you could come together over lunch or dinner and then have family time. Try to do this at least every other week but do have special time once a week with each child. It doesn't have to be long but it is just as important.
It's very common that an older sibling feels left out and jealous of the younger one so they act out because they feel as though they have to compete for your attention and if it continues, they will feel you love the younger child more than them.
This can cause more than just sibling rivalry down the road. I experienced it with my older sister and I know several others who have also.If you try this please let me know how it works out after a couple times. Thanks and good luck!
P.S. about the bedtime, I don't know of what you can do for when she wakes up, except that it might be growing pains-my daughter gets them a lot. but to decrease the amount of time you spend putting her to bed, weather permitting, get them outside to play for at least twenty to thirty minutes every night about an hour and half to two hours before bedtime. Some kids might need more time. Also establish a "steadfast" routine. I used to read a short story to my daughter every night at bedtime. Or if I didn't feel like it I would sing her a lullaby. I also put a cd player in her room- if you have to put it up high- and i play a musical lullaby cd for her almost every night. Don't use one with lyrics for them to sleep to that can have more abrupt fluctuations in the music and wake them up. Also, reading to them or singing ot telling them a story is a nice quality time to spend with them each night and it will help reassure them that you love them and they have your attention to sleep easier.