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If you are feeling anxious, try focusing on calming your body (deep breathing, hot beverage, warm blanket etc) and watch your thoughts calm. It's much easier to do than the other way around. Our brain works bottom to top, not top to bottom, which is why it is so hard to think your way out of what you feel.
The myth that comforting your child will "spoil" them is not only emotionally harmful but also creates an altered brain state that leads to higher levels of stress and mental illness in adulthood, giving them compassion and comfort will only help them develop a healthier brain function.
The idea of toughening up your children to deal with the world only makes you their first bully, stripping them of their sense of belonging with you; treat your children with respect and connection so that they instinctively protect themselves from unkind and cruel treatment.
Learn how to deliver an ultimatum with kindness and honesty, and set healthy boundaries in your relationships, in this insightful video.