Your baby only does it with you.
She is 1.5 years old, almost.
Let her be.
You cannot "ignore" the eldest child.
Please also, talk with your eldest child. Explain to her/him, that baby is very young and they cry. But that you value your eldest and will give him/her more time.... and that you love him/her very much. And that he/she is always your first "baby."
When I had my 2nd child, (my kids are 4 years apart), I would spend a TON of time on my eldest.... and explain to her, routinely, each month, about how baby brother is developing and changing and his developmental "phases." I explained in simple terms in a way she could understand. I did this SO that... my eldest did NOT feel, that the baby was more important or that her baby brother was just being irritating on purpose. It made us closer, she then had an understanding of "babies" and how they are and develop, and that made her more aware... of what Mommy is doing too, and she felt "smart" and informed about babies.
When her baby brother would cry... she would (with the information I taught her), tell me "Mommy, I think Johnny is hungry..." or "I think he is tired.... " or "I think he misses you..." But in no way, did I make her feel responsible for my being busy, with both of them.
But, my 2nd child routinely napped. And that is also when I spent time with my eldest.
Your baby is crying/fussying a lot.... so at times you just need to let your baby cry.... but put her in an area on the floor, perhaps in a Play-yard, and let baby be there... but while playing with your 4 year old.
And even amongst the "chaos" of toggling between your baby and 4 year old.... make sure, that you talk with your 4 year old, recognizing him/her, and complimenting him/her on how patient he/she is being.
ACTUALLY TELL YOUR Eldest- "Thank so much for being so patient with Mommy and baby. I do notice you know... what a great sister/brother you are even when Mommy is busy. But I know you are still a child yourself... so never be afraid to tell Mommy how you feel. I am here for you."
I did that with my Eldest all the time. It really helped. It reassured my eldest. Kids, NEED TO HEAR that from their Mommy... once they have a sibling.
"Quality time" with the Eldest, is thus not just in doing something with them face to face... it is ALSO, in how you talk with them, and acknowledge them and that you understand what they are going through too and validate them.... as the Eldest and as Mommy is so busy.
There were times where my eldest and I would be playing together, with baby brother on his floor play mat near by... him babbling to me and what not, but I would just say out loud "Hi Johnny, Mommy is right here. I am playing with sister now. Don't worry, we are right here. It is sister's turn now, sister needs loving too..." and then continue on. That way, baby is hearing you but at the same time the eldest child is seeing AND hearing Mommy, acknowledging the eldest. So they do not feel left out and that the baby ALWAYS takes more priority over them.
It takes a lot of toggling... both in person and verbally and emotionally and visually... for the eldest child and the baby.