I was thinking that since the MC mentioned Nicole used to be stern but is now more relaxed with the whole situation, letting us know she doesn't let anyone trample over her or take advantage of her.You're somewhat correct about the "Nicole Payment". However, I wouldn't call it "sexual favors" but it's pretty hard to narrow down the proper name/term of the early parts of the relationship. I can see your point that the starting point of MC's (Us) and Nicole's relationship isn't that strong or weird but as we progress throughout the game the foundation between Nicole and MC (Us) becomes stronger, regardless which route you're on. It starts out as seducing, sex to fulfill the lust of both characters but later it becomes love because in some of the sex scenes in "A Mother's Love" Nicole willingly wants to make love to MC (Us).
Regarding about Nicole's pride, ever since the start of the game her pride isn't that strong hence in some sex scene she's easily persuaded by the MC (Us). But as we progress throghout the game, especially in the "love route", we begin to respect her pride or decisions.
For instance, when she was secretly modeling, Joshua tried to have his way with her. Despite having the potential to gain something good in exchange for engaging in that affair, she was strong and immediately rejected any advances. However, with the MC, instead of exposing him for his scummy attitude right from the start, she played along with almost no resistance, and in this case, there is no real benefit for her to accept this.
That part feels as if, had we been able to read her thoughts all the time, she secretly wanted it to happen. Maybe not hiding it due to pride, but just to avoid feeling too guilty for falling for the MC and stealing him from her daughter.