Assalam Alaykum
The belief in al-wala’ wa’l-bara’ (loyalty and friendship vs. disavowal and enmity) is one of the most important basic principles of Islam. Just as faith increases and decreases, so too people vary in the extent to which they adhere to this important principle, and their adherence to it increases and decreases. But if this principle is destroyed completely in a person’s heart and he does not do what it implies, this means that faith has been destroyed entirely as well, and faith is the basis on which he loves the close friends of Allaah and hates His enemies. This principle is indicated by a number of verses in the Book of Allaah and ahaadeeth from the Sunnah of the Prophet (peace and blessings of Allaah be upon him). These include the following:
Allaah says (interpretation of the meaning):
“You (O Muhammad) will not find any people who believe in Allaah and the Last Day, making friendship with those who oppose Allaah and His Messenger (Muhammad), even though they were their fathers or their sons or their brothers or their kindred (people). For such He has written Faith in their hearts, and strengthened them with Rooh (proofs, light and true guidance) from Himself. And He will admit them to Gardens (Paradise) under which rivers flow, to dwell therein (forever). Allaah is pleased with them, and they with Him. They are the party of Allaah. Verily, it is the party of Allaah that will be the successful”
[al-Mujaadilah 58:22]
“O you who believe! Take not for Awliyaa’ (protectors or helpers or friends) disbelievers instead of believers. Do you wish to offer Allaah a manifest proof against yourselves?”
[al-Nisa’ 4:144]
With regard to praying for her to be healed from sickness, this is permissible if it serves a purpose, such as if one hopes that she will become Muslim and that her heart will be softened and so on. This is indicated by the hadeeth of the Sahaabi who recited ruqyah for the chief of a tribe who had been stung by a scorpion. and Praying for healing comes under the same heading as ruqyah.
Indeed it is permissible for you to visit her during this sickness, because when a person is sick her heart is softer and is more likely to accept the truth. The Prophet

(peace and blessings of Allaah be upon him) had a Jewish boy who used to serve him, and he fell sick. The Prophet (peace and blessings of Allaah be upon him) came to visit him; he sat by his head and said to him: “Become Muslim.” He looked at his father, who was present, and he (the father) said to him: “Obey Abu’l-Qaasim (peace and blessings of Allaah be upon him).” So he became Muslim and the Prophet (peace and blessings of Allaah be upon him) went out saying, “Praise be to Allaah Who has saved him from the Fire.” Narrated by al-Bukhaari, 1356.
Ibn Hajar said: This hadeeth indicates that it is permissible to employ a mushrik as a servant and to visit him if he falls sick, and this is a form of kind treatment.
<wasalam>