Salaam alaykum warahmotullah.
Does the rights my mother has towards me and that which I have towards her changes if she becomes a Christian? My Mum became a Christian by marrying a Christian after divorcing my Dad. When I preach to her and reinform her that Islam is the right religion with evidences and examples from the Quran and Hadith she gives excuses of her husband that she has to follow her husbands religion. I pray and always ask Allah to return her soul and heart back to Islam.
What can I do or say more to help her understand and reason?
I would also appreciate if you can leave an hyperlink to a fatwa about the rights of Parents especially that of the Mother while answering this question. It's been really difficult these past years thinking of her and her situation.
Thank you.

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.

First of all, we thank you for your concern about your mother, and for being keen on knowing your rights towards her. You have done well by being keen on being kind and dutiful to her, may Allah reward you and fulfill your aspiration.

There is no doubt that one of the best things by which you will be dutiful to your mother is by endeavoring to enable her to repent, to follow the guidance, and to return to her senses. You are right in always supplicating for her; so just continue doing that. The hearts of the servants are in the Hands of Allah, and He is the One Who can guide her.

Allah Says (what means): {And Allah guided those who believed to the truth concerning that over which they had differed, by His permission. And Allah guides whom He wills to a straight path.} [Quran 2:213]

Allah commanded us to be kind and dutiful to our parents – especially to the mother – even if she is not Muslim; Allah Says (what means): {But if they endeavor to make you associate with Me that of which you have no knowledge, do not obey them but accompany them in [this] world with appropriate kindness and follow the way of those who turn back to Me [in repentance]. Then to Me will be your return, and I will inform you about what you used to do.} [Quran 31:15]

Asmaa’ bint Abu Bakr narrated “My mother came to visit me while she was an idolater at the time of the Prophet so I asked him, ‘My mother has come desiring my kind treatment. Shall I keep ties with her?’ He said, ‘Yes, be dutiful to your mother.’” [Al-Bukhari and Muslim]

Al-Qastalaani said when interpreting this Hadeeth: “…Shall I keep ties with her?; means being kind dutiful to her, or that she [her mother] is repellent from Islam and she hates it; and she asked the Prophet whether she can be kind and dutiful to her and he said: “Yes.”

We recommend that you continue advising your mother, and perhaps it is better to delegate some scholars whom you hope that she might listen to, so that they will clarify to her that what she has done is wrong as she married a non-Muslim while she is a Muslim. This is indeed forbidden according to the consensus of all the scholars, even is this non-Muslim is a Jew or a Christian.

Allah Says (what means): {And do not marry polytheistic men [to your women] until they believe. And a believing slave is better than a polytheist, even though he might please you. Those invite [you] to the Fire, but Allah invites to Paradise and to forgiveness, by His permission. And He makes clear His verses to the people that perhaps they may remember.} [Quran 2:221]

On the one hand, the fact that your mother apostated from Islam is a more serious matter as this invalidates her deeds and necessitates eternal Hellfire.

Allah Says (what means): {And whoever of you reverts from his religion [to disbelief] and dies while he is a disbeliever - for those, their deeds have become worthless in this world and the Hereafter, and those are the companions of the Fire, they will abide therein eternally.} [Quran 2:217]

Also, her believing that a wife has to follow the religion of her husband is a great ignorance from her. Apostating from Islam is absolutely forbidden and we have already mentioned the threat about apostasy, regardless of whoever did this, whether she is a wife or anyone else.

If she repents and returns to Allah and re-embraces Islam, then praise be to Allah; otherwise, you have still to be kind and dutiful to her as we have already mentioned even if she remains as a non-Muslim.

For more benefit on being dutiful to non-Muslim parents, please refer to Fataawa 350689, 260962, 332665, and 92093.

For more benefit on the absolute prohibition of a Muslim woman marrying a non-Muslim man, please refer to Fataawa 90619, 87151, 274252, 124877, 84265, and 88406.

For more benefit on Apostasy, please refer to Fataawa 174509 and 375391.

Allah knows best.