It's not that rare in the real world for kids to get jealous when anyone is dating their parent. It's usually just because they don't want to share the attention and love they get from their parent, they're worried their parent might not have enough left for them if they have a new romantic partner. Kids also often feel the same thing when they get a new sibling.
Children, and I mean children not kids, tends to feel conflicted when their parents attention is no longer just theirs. When my dad had a girlfriend, he raised me as a single father all my life, it felt like he's ready to move on with his life, and in my point of view as a careless teenager, I'm not going to be part of the new life he's creating with his new girlfriend and the child he had with her. I was feeling so rebellious that time so I left my house and travelled to another state where my mother's family lives.
The story is interesting, it seems like people are angry with the red haired girl for both understandable and not understandable things. Yes she assumes so much without MC even confirming a relationship and seems whiney but she's a strong and relatable character for people who want to better their skills.
The main issue personally is the weird response that MC's daughter gives when she finds something related to MC being with a woman, weirdly angry.