All perfect praise be to Allah, The Lord of the Worlds. I testify that there is none worthy of worship except Allah, and that Muhammad is His slave and Messenger.
The wife has the right to have an independent accommodation, as stated in the Fiqh Encyclopedia:
"The wife has the right to have a separate housing that has its lock and its facilities, even if it is within the same house ..." [End of quote]
The jurists indicated that the criterion for an independent house is to have an independent kitchen and bathroom/toilets.
Sharh Al-Khurashi ‘ala Mukhtasar Khaleel, from the Maaliki School of jurisprudence, reads: "(The house should be) independent with its facilities and benefits, such as toilets, a kitchen and other needed matters ..." [End of quote]
Also, Tuhfatul-Muhataaj, in the Shaafi’i School of jurisprudence, said about the independent housing: "What is meant is that they should not share something that could lead to disagreement….." [End of quote]
Since, the kitchen is shared between your wife and your family, then the housing is not independent and your wife has the right to ask you for a kitchen that is independent from the kitchen of your family.
We advise you to try to convince your wife to live according to your ability. Many people got married and lived with their families until Allah facilitated the matter for them and they moved to independent homes.
So, if she insists on her right and requests a completely independent housing, including an independent kitchen, then you may look for another wife who would accept your condition; this is better for you than overburdening yourself with something that you cannot bear.
Allah knows best.