If a woman is not required to pray in a minyan because her prayers are stronger and more direct, why must she have a minyan to say kaddish in an orthodox shul? If there is minyan that day, what is the alternative. Maybe the way I’m asking includes some incorrect assumptions, so looking forward to your response. Thank you in advance.

Shalom! Your assumptions are correct but just partial. There are several reasons why women are exempt from praying in a minyan, including those which you mentioned and also that they shouldn't be bound by the pace of others- but can pray more from the heart; but also, in order to free them for family obligations (which are no less important))- e.g. to take care of children and nurse infants, etc. and to make sure that those important family needs don't "fall in between the chairs". Accordingly, the Avudraham explains the Torah exempts women from such mitzvot that can easily disturb the family needs. Accordingly, women are exempt from communal prayer and are also exempt from saying kaddish. On the other hand, kaddish and communal prayer are (!) very important, so on a national level, it's enough to obligate the men. If a woman wishes to participate, she may, but halacha gives her the flexibility and leniency which enables her to choose, according to the needs of her family, and according to where she will pray better!