All perfect praise be to Allaah, The Lord of the Worlds. I testify that there is none worthy of worship except Allaah, and that Muhammad is His slave and Messenger.
First of all, may Allaah reward you for being keen to be kind and dutiful to your parents and for reciting Athkaar (the mention of Allaah), so may Allaah increase your zeal and make you more pious.
As regards the issue of mentioning Allaah coinciding with the preparation of food for your father, then you should give priority to the preparation of food for him as this is an act of being dutiful to your parents, and being kind and dutiful to one's parents comes in priority over the Athkaar in case of conflict.
This is, of course, if we presume that they conflict, otherwise it might be that there is no conflict at all; for example, if you memorize the Athkaar, you may recite them (by heart) while preparing the food. Also, you may recite them after preparing food especially that these Athkaar take only few minutes. Indeed, Ibn Al-Qayyim clarified that the timing for Athkaar of morning and evening is between the Fajr prayer until sunrise and from ‘Asr prayer until sunset, and his evidence for this is the saying of Allaah (which means): {And exalt Him morning and afternoon.}[Quran 33:42]
Allaah Knows best.