I mean, that's what makes her interesting. Erika isn't a model parent at all. She frequently gets absorbed in her work, much to Tita's detriment. Hell, she was gone for a few years, basically dumping Tita on Russel.
I don't know. I mean, she's funny and all but I don't have a lot of sympathy for her overprotective behavior. She goes off on Agate and the whole time, I wanted to scream, "Yeah, but he was actually THERE. Where the hell were you?"
Hopefully, the game explores this further because right now, it feels like her and Dan dumped Tita on Albert because it was more convenient for them.
And that leads us to her door, where we see that Erika and Tita are on completely different wavelengths. Erika obviously loves Tita, but she treats her like she's a little doll and nothing more. She fawns over how cute she is, but she doesn't take her seriously - not when Tita shows interest in the new project, and not when Tita explains how she could use her experience to help with it. Erika doesn't think Tita is ready to help - she's been absent for the last several years, and it's plainly obvious. Her fascination with engineering and science has created a rift between herself and her daughter.
I'm sure you got all that when you played through the game. But Erika's faults don't make her a bad character (maybe you think she's morally bad, but that's a different argument altogether). Instead, her faults make her believable, and it's what makes her (in my opinion) an interesting and compelling character.
When I was growing up, I went to school in the suburbs, but my dad worked in a rural town about an hour and a half away. It was so far that he would live in that town and only see the rest of our family on Wednesdays and during the weekend. Later, he ended up commuting three hours every day so we could see him more often. But he was so tired that most days he would come back home and immediately go to sleep. Obviously, this isn't as drastic as Erika leaving Tita for years, but the entire sequence really nailed the disconnect between parent and child.
This is what makes me love the Kiseki series so much. In almost every other game, Erika would be reduced to "Party Member 6's mom who's been gone for a long time". They might have left the Agate jokes in for comedic relief, but they almost certainly wouldn't have been able to convey that Erika is a character on her own. That she has her own motivations and aspirations, and that her goals have been interfering with her personal life. Erika has more characterization than entire casts of certain JRPG's.
And she's a side character that gets like half an hour of screen time.
but uh yeah "flawed character" =/= "bad character"
Edit: added spoiler tags