K.C.
Oh honey, she wants attention and negative is usually the fastest and easiest way to gaurantee she'll get it. This happened in my family. My older son was about 2 and my younger son was a couple of months. My older son wanted my attention so badly he would dig his nails into the baby's hand. These things only happened when it was just me, never in my husband's presence. There were other things he did, but that seems to stick out in my mind. It's been 6 years and another child later, so forgive my Mommy memory.
Find someone you trust who can stay with the baby for a short time for that one on one your oldest. Even someone who can come to the park or mall with you, if you don't trust leaving the baby alone with that person. You have to ask for help. I went through this alone, we moved away from family and our support system when baby #2 was 7 weeks old. I didn't know a soul I could trust. Do you have a family member, Mom or MIL who can stay with you a couple of days while your husband is gone?
As for the screaming, been there (big sigh). I have a couple of suggestions. One is to take a Mommy time out. Remove yourself from her sight for a minute or two, gather your thoughts and come back a little calmer so you can speak rationally without screaming. This is hard to do in the heat of the moment, but so worth it. Another is to try giving hugs/kisses instead of screaming. She totally expects you to yell, if you hug her, she'll be shocked that's she's not getting the "normal" response, that might be enough to get her to listen to you. My best friend recently told me that she asks her son, "Do you want a punishment or do you just need to sit on Mommy's lap for a minute." Of course he always picks the lap and it diffuses the situation. I'm planning to try this last one myself.
Google Mom meet up groups in the local area to find a playgroup for your oldest. My computer's acting up otherwise I'd have posted a link.
I hope this helps!
I hope this helps.