Is it permissable to eat food cooked on Shabbat for the sake of honouring ones parents?
It is hard for me to understand your question, therefore I can only answer you generally.
We may not desecrate the shabbos in order to honor our parents, in fact the torah says this specifically ( Leviticus 19-20) איש אמו ואביו תיראו ואת שבתותי תשמרו , and Rashi explains that this means that even if a parent asks us to desecrate the shabbos we must not do so. Therefore the food would be the same as any other food that was cooked on shabbos and may not be eaten.
Have a good Shabbos