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Because we identify with our attachment loves (kids, spouses, parents, best friends etc) we are more likely to treat them the same way we treat ourselves.
If you find it easier to be kind and generous with strangers or acquaintances, it is likely about your own lack of self compassion, not something with your loves.
Try being more gentle with yourself and watch what happens with your instincts towards the people who matter most.
Learn how to foster secure attachment with your child by being a consistently responsive and connection-focused parent, and don't beat yourself up for not being perfect - the important thing is to focus on repairing and staying dedicated to the relationship.
Learn the power of modeling self-compassion to your kids, as it inspires authenticity and problem-solving, and helps them develop their own self-treatment based on how they see you treat yourself.
Learn how to set compassionate limits with your child in a way that benefits their brain development and reduces reactive responses to emotions, with the timing varying depending on factors such as age, hunger, and consistency.