Congratulations on your new addition and thank you for rescuing.
Did you adopt her from a rescue or a shelter? If she was in rescue have you tried to contact her foster home and see how they handled her? You are wise to recognize this an a problem and glad to see you are trying to address this issue.
I think that what Izzy is doing is not attaching herself to you but showing possessiveness which is a big problem. My thought and suggestion would be to ignore
all the pups when you first walk into the house. Once you put your things down and settle in
then greet each one and make Izzy wait her turn. If I were you I would not even allow her to be the first to her food bowl. Give the attention to the others first. She needs to be put into her place in the pack and recognize that her behavior is inappropriate. If she bites immediately put her down and ignore her. When she is on your lap and the others approach you put her to the floor as well. Stay consistent with how you are handling the situation. Do not allow her to dominate you or the other three. If you do not stop this behavior NOW it will continue to get worse and there will be fighting. Good luck and let us know how it is going with Izzy.