I spent a year trying to pussyfoot my way through a divorce thinking that if I was reasonable about it, somehow that would be "best for the kids" and the sake of our coparenting relationship.
My xAH eventually found an attorney who took me for everything he could.
Your parents are right - don't fool yourself into thinking you can control the situation by behaving one way or another. Try to get it done, and get what you deserve. And do not let anyone try to convince you that you have no chance at sole custody.
My first legal consult (I did it while I was on maternity leave) told me to pursue sole custody and act immediately, because I was much more likely to get it when the kids were still babies. I often look back and wish I had taken than advice.