One doesn't have to treat a person like their son to be described as "motherly/fatherly", calling her mom/mommy it's because we are chatting in a thread about a lewd game, but regardless, Bella has motherly qualities (not speaking of the juggs

), that some women have and some don't.
The episodes cited (haircut, kiss on the head, etc...) don't make her the MC's mom, but do display that certain predisposition, one that for example Jade doesn't have.
Jill is motherly, Maya isn't (she actually need a fatherly figure), the difference between being a giving person and a self-centered one, and one of the attributes of being a mother/father is the giving aspect.
Does the interaction change during the game? Yes, nobody is going to say that bringing out some anal beads to have a full on anal evening is a motherly attribute, but that's why she isn't the MC's mom and doesn't want to be, but also (imo of course) why I do believe there's some child loss trauma behind her secrets.