birthday party for my 5 years old daughter

We want to organize a birthday party for my 5 years old daughter, because she wants to invite some friends to celebrate. We were not sure of the date. We thought of the 30th of May, because this is her birthday. My mother wanted to join and started to organize games to play with the children.
Then my father asked us if we want to celebrate this birthday with my brothers and him (my father and my mother are divorced) the 30th of May. I thought it would be nice to have a rare opportunity to see one of my brothers who is living far away from us. So I called my mother to tell her we will organize the party with my daughter’s friends one week later. She said she was not free.
Yesterday my father told me that my mother told him that I changed the date because I don’t love her. My father said she was really upset.
Finally he invited her to the party with the whole family. I called her to apologize.

My thoughts: My mother is weird. How can she think that? This has nothing to do with me not loving her. We have a very good relationship. This is so childish of her. I’m fed up with all this organization. I don’t even want to go to those parties anymore. I’ve got too many things to do. This is just an extra burden. Now I’ve got to be very cautious with not upsetting my mother.

I know intellectually that my mother being upset is not a fact and that I’m not responsible of her feelings.

C My father tells me “your mother thought that you don’t love her”
T she is so childish
F irritated
A ruminate, think to change the calendar again, think not to come to the family party, don’t show up with love to this party, isolate from my family, judge me and my mother, pout during the party, accuse my mother to cause my unpleasant feelings
R I am childish

C My father tells me “your mother thought that you don’t love her”
T I’m a bad daughter
F guilty
A don’t show up to the party, apologize, find a way to make my mother happy, accuse myself, criticize myself, act unnatural with her
R I take responsibility for my mother’s feelings and put myself in an impossible situation

C My father tells me “your mother thought that you don’t love her”
T The nightmare comes back
F depressed
A remember when my mother was so depressed in the past, find evidences of the reality being weird and nightmarish
R I create a bad story that is not real

Could you help me to move forward? Thank you so much for your amazing feedback.