Wa `alaykum as-Salamu wa Rahmatullahi wa Barakatuh.
In the Name of Allah, Most Gracious, Most Merciful.
All praise and thanks are due to Allah, and peace and blessings be upon His Messenger.
In this fatwa:
1- Muslims are ordained to rule according to the Shari`ah laws.
2- Those Muslims who are living in a non-Muslim country should follow the laws of this country.
3- They should take all the legal means that enable them to gain their rights and relief their sufferings.
Responding to your question, Dr. Muhammad Salama, PhD in Islamic Studies in English and an Assistant Professor at the Faculty of Islamic Science, Al-Madinah International University, states:
In principle, ruling by other than the Shari`ah laws is a grave sin, for those who do so are described in the Qur’an as “disbelievers“, “wrongdoers“, and “ungodly” (Al-Ma’idah 5:44, 45,47)
When Muslims live in a land governed by non-Islamic laws, they have to go through all legitimate ways that enable them to get their rights or at least alleviate their sufferings.
Participating in elections and attempting to assume some political positions is a way to this legitimate purpose in democratic countries. The principle that governs such situations is to strike a balance between the benefits achieved and the harms to be suffered from such participation.
Accordingly, those members of your family who have assumed such political positions must have the good intention of helping their Muslim community and do their best to enjoin what is right and forbid what is wrong as far as they can.
If they can do so, they would certainly be rewarded by Allah Almighty, even if they sometimes rule by secular laws based on the principle mentioned above, for the benefits that Muslims gain in this case outweigh such wrong practice.
Allah Almighty knows best.