I've played since I was 7, started because my parents wanted to do the weekly shop in peace for an hour without me pestering and being a nuisance, so I was sent to coaching. I grew to love the game, got better and ended up gaining my coaching qualification myself.
I've always said that any child I had, i would never push into playing, tennis or any sport. If they wanted to play, fine, but i would never force them. If they asked for help & to play, I would be there for them. I now have a little girl coming up to 3 and I bought her a tiny 17" racquet which she sometimes pushes the ball around the grass in the back garden, but that's it. I throw to her but then she usually gets distracted by the swing or the trampoline. And that's fine too.
My point is, I never had the tyrant of a father, he just wanted me to play whatever I enjoyed, and that's how I am with my daughter. Also probably why I've never won a Slam. Agassi's dad was a major factor in his success, but a lot of it has to come from Andre himself being super talented naturally. There would've been a point where he'd have thought I don't need my dads permission or harshness, I want to play. Perhaps the prize/sponsorship money helped that! But you also have to look at it that if his dad didn't push him, he wouldn't be where he is now, with Steffi and their kids. If my daughter wants me to coach her I will, but not to the detriment of it ruining our relationship. Pros & Cons for both sides.