Hi - yes, actually! I just noticed it last night for the first time when I had some triplets age up and I noticed the notations in the relationship box. I hadn't even been really aware of them because I hadn't really focused hard on using the parenting interactions until these kids. I'm sorry I can't recall the exact wording (I can check tonight though if you want) and with one kid it was something like "Very Involved" and the other was more like "Pretty Involved." I think the difference with this particular parent was he had the Super Parenting aspiration and I was trying to get him the last 3/4 of the tenth point during the last day or so before the triplets aged up, and also to get him into Super Parent mode which is also one of the milestones. He was absolutely spamming any parenting interaction that would come up, like satisfying chat, ask about phase (they were ALL having different phases, grr), influence to wash dishes or whatever else was available. When these guys were kids he did a lot of the firm discipline actions, but actually very few of them for two of the three triplets or after they turned teen, because they were already sickeningly well behaved and there wasn't much to discipline them for. :P
I didn't get a chance to check the third triplet (she died almost immediately after aging up, but that's another story) but in her case I was trying to build the negative personality traits, so he didn't discipline her much nor did she get subjected to the parental interaction spamming because I was afraid that was going to drop her out of range to get the traits I wanted. But the "very involved with" triplet was definitely the one that received more of the spamming than the "pretty involved" because I kept her home from school the last day for that exact purpose.
So I'm presuming that relationship marker is built not just on punishments/discipline, either positive or negative, but also on the rest of the general class of parenting interactions. If you were focusing on the harsher elements you might have avoided some of the others since majority of them seem pretty positive.
I'm sure others out there have more experience than I do on this because like I said, I only really started focusing on this gameplay with the current family, so a lot of it is still new to me. :)
ETA: I just checked and the two remaining triplets have "Daddy's Girl/Boy - the best relationship with a relaxed parent." The deceased one (who invited her dad out to lunch) has "Provided Happy childhood - a great relationship with a relaxed parent."