M.P.
I'm wondering if your daughter has needs to learn new ways to relate with her brother and is having difficulty doing this. He's become more independent, able to walk and have strong preferences of his own. She's become frustrated and lashes out physically. Because she tends to be too rough by nature her frustration comes out in scratching and hitting.
I agree with Peg M. The book about talking and listening with our child might help you be able to learn from her what she's thinking and feeling. Acknowledging her angry thoughts/feelings will help her be able to learn how to manage them. Being able to talk about how she feels will make her have less of a need to act them out.
Your son is at the stage in which he's comfortable playing by himself or next to another toddler. Your daughter is wanting to play with other children, especially with her brother. She needs help learning how to deal with that difference in expectations.
She is developing a different relationship with her brother because of his increased independence and perhaps needs reassurance that he loves her even when he doesn't want to do what she wants. I suggest spending time, if you don't already, playing with the two of them, modeling how to play side by side with the littlest one and saying out loud what her little brother may be thinking Be sure to include his possible thoughts about her such as saying I like having you next to me but I want to play by myself.
Of course your daughter feels some jealousy that plays into some of her actions but not all of them. She's also at an age where she is learning new skills and is aware of feelings in a different way. She can now verbalize her feelings while her little brother cannot. Spending time with her alone, as you suggested, is a good idea. During that time you can use some of the ideas from How to Talk so Your Child can Listen and vice versa with her. It really does make a difference in how we word things.
Perhaps you can teach her to come to you when she's having difficulty with her brother. Remind her to use her words even tho brother does not respond by doing what she wants. If you're nearby you will pick up on her tone of voice and intervene earlier. Give her a way to vent her anger. I often tell my grandchildren to run to the corner and back or count how many times they can jump up and down. By the time they're thru they've often forgot why they were angry.