Pejoratively yes, because she's disgusted and/or annoyed by her but I wouldn't say that she used that word so that Vicky would do what she wanted. That's what blackmail was for.
Anyway, saying that she's doing it for herself/for appearances is overinterpretation. I would argue that wanting her son to be more responsible and successful is a sign of more caring about him than Victoria's hedonistic approach where she says
"let him have fun while he's young". That's easy for her to say when she has a successful and intelligent son who's to become a doctor while Grace's son wastes his time on whores/sluts with some photography on top. What mother (who isn't a whore) would like her son to be a leech/parasite that thinks about sex only?
If she really was the person you claim she is, she would have never allowed Ian to go to a public school (imagine what other snobs would say when they would learn Grace's son wouldn't get best education available) or for Ian to be friends with Edwin or for Edwin to come with them on vacations or for letting
Victoria a whore to come to Thanksgiving even though she clearly despised her (the answer here is obvious, Ian asked her to invite Victoria so she did because she loves his son). Nothing adds up here unless we assume that she loves her son (she even says so and I see no reason to doubt that considering the above).
Grace had plenty of chances to tell Victoria what she thought about her but she didn't until she felt she had no choice. She was amicable the whole time when talking to her except for that one outburst (but she quickly recovered herself and became calm again) which I interpret as a sign of love (maybe warped but definitely love, she's clearly jealous of Victoria).
As for August, again it's overinterpretation. From where I stand it seems to me that August wants a successor and since he doesn't have the alternative (AFAWK) he went with Hana. He had appeared only recently ignoring her daughter most of her life. I'm not saying he's not genuinely pursuing her affection (he obviously is and he cares about her) but that "entire game" that you mentioned is what...? A year + 3 weeks (at best since we don't know when his pursuit started)? Meanwhile Grace cared for her son his entire life, that it wasn't what Ian wanted is irrelevant.
Not to mention that if letting your daughter work in the brothel dressed up like this is an affection of love then I have bad news for Hana:
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And it was August's idea...
P.S.
BTW, I wonder what fluids of Hana did August use to test for DNA to see whether Hana is his (I refuse to believe that he used her hair) :]. Because let's be honest, knowing the industry Hana's mother was in I'm sure he wouldn't go by Hana's mother word only.