Coercion, including covert coercion imposed with a soft voice and loving words, is deeply disconnecting, and it certainly does not feel compassionate to the person on the sharp end. What seems to be called ‘Self-led parenting’ is a far cry from the deeply respectful, non-coercive spirit of the Self of IFS when they are talking about adults.
When you struggle against or take a coercive approach with another person, the natural response of that person is to defend their corner and fight back. The same happens inside our own minds. When you are fighting a part of your own mind, that causes the part you are trying to stamp out to dig in, to entrench itself, to defend its corner more vigorously.
How to be emotionally-intelligent in our dealings with these anti-rational parts of our mind, meeting them where they are, at their own problem situation, seeing how it feels for them from their perspective, rather than just barging in with the critical arguments that seem so rational and unanswerable to us from our (or another part’s) perspective.
Such questions are in effect asking how we and our children can solve the problem created by us in effect having a visceral aversion to our children innocently enjoying themselves learning. Why is that the case, and when we are in such a state, what can we do about it?
If you think your child needs you, maybe experiment, tentatively trying different ways of being there for her and making sure she knows you are there for her and want to do what she wants and not what she does not want.