Albeit both sentences don´t sound pretty usual to me, I wonder whether the second one could´nt be changed to: My mother remains in the kitchen in order to cook dinner.
I didn´t intend to suggest the kitchen as mother´s default place in general. But where else could she prepare the lunch and cook it…unless she had planned a BBQ…on which certainly father´s default place was in front of the grill (not upon)
Please note the spelling of the word ‘grammatical’. Also, I would rephrase your question like this: ‘Is the following sentence grammatically correct’?[YSaerTTEW443543]