In Islam when it comes to parenting, does the father have more authority/right over the children than a mother?

I have a situation where the father gets upset on Eid celebration and the children birthday because the food generally that gets served on the day is sweet. We have stopped having birthday celebration at home for the family to avoid making him upset. We also do not attend birthday celebrations and limit food when attending Eid gatherings. We also do not serve sweet dishes at home or to our guests to avoid making him upset. He says it is better stay away from unhealthy habits. He considers the wife as weak and incapable of making decisions when it comes to the children and the husband has more authority over the people of the household.

The article that the father has shared with me is from Ayatollah Ibrahim Amini, ‘Duties of women in Islam’.

Quoting "…it is in the best interests of the family that women accept the supervision of men and perform important affairs after consulting with their husbands and, in the event of a disagreement, accept their husbands’ judgment."

What is the best way to address this situation?

Indeed the father has a special position because of the responsibility placed on him to maintain the family and act as a guardian.
However, Islam does not stipulate that he always knows best or that what he dictates is an absolute law. Rather, Islam teaches us that there should be cooperation and mutual respect in family matters and that in certain places, each should defer to the other.