My Chloe girl

My Little Chloe girl is a sensitive child. She notices feelings. She is a nurturer. She is caring and loving and sweet. I love her more than I can express in words.
Last night she went to sleep with Grandma, while I was at Derby practice. Which is unusual. She normally makes herself stay awake until I get home, or falls asleep on the couch or in the chair with Grandma, if Daddy isn't home. She continued to stay asleep in her bed after Grandma got out of bed, which again...unusual. At 2:00 am I heard screaming from upstairs. Terror in her voice as she was in her sisters' room telling them she didn't know where Mommy was. I ran lightning quick to her. She was afraid, the triplets were afraid. It took me about thirty minutes to get them all calmed down and laying back in their beds. I took Chloe downstairs with me. She continued to sob. I told her to tell me where she thought I was. All she said was I just don't want to be by myself. I feel horrible.
We have been working with her to be more independent. To try to do normal tasks on her own. Things like brushing her teeth, going potty, getting things from her room. She is horrified to be alone. She always wants Mommy, Daddy, even one of her baby sisters to accompany her. She refuses to sleep alone. She wakes if Matt or I exit the bed to go to the bathroom in the middle of the night. Which is obviously interrupting her slumber...the rest she needs.
The last several school days have been extremely rocky at drop off. She cries and says she wants to be at home. She doesn't want to go to school. She gets so upset that she literally cannot breath. I called her teacher last week and expressed my concerns. Chloe had shared that there are three little girls not sharing and not being nice. I also talked with her teacher about this. They had an entire school "talk" and role played about feelings and being friends. I thought that was great. Chloe was fine on Tuesday when she went. Smiles and all. Today however, she was so upset again that I questioned taking her at all for the rest of the year. When we arrived at school she walked in, put her "pack pack" away and then walked up to where I was signing her in and just melted down. She was so upset I could hardly understand her. She cried for her Daddy. Just kept repeating she misses her Daddy. I felt so bad. I picked her up and hugged her and then her teacher came over and asked her is she wanted to go outside with her to play. Chloe agreed and went to her. I called the school when I arrived back home to see how she was doing. Talked to her teacher who told me that she seemed fine and that she was swinging with her bestie Maria. I feel better, I guess. I promised her I would have Daddy pick her up from school.
My heart hurts. Matt works so hard to take care of all of us. Her works a minimum of 60 hours a week, many weeks more. He wants his family to be taken care of. He feels badly that he is away. I know he misses the Beauties so much it hurts. Which is why he went to nights. He sees them more. I wish I could explain it to Chloe, but I know she is too little to fully understand.
I am at a point where I don't know if I need to go and talk with her pediatrician about things. She seems to have some definite separation issues and is scared to be alone. I know the last couple years she has had a lot to adjust to. Mommy being in the hospital for 9 weeks, Mommy being in the hospital for 4 weeks with her sisters, having not one but 3 baby siblings come home....so much for a little girl to handle. We spend alone time with her as much as we possibly can. We take her and do "big girl" things with her. We have Chloe and Mommy time and Chloe and Daddy time. I just want what is best for her. Has anyone every experienced anything like this? I need suggestions, advice. I just feel like I am failing her somehow.