She wants to take the notebook of her servant on the grounds that she taught her what is in it

Firstly: 

Bringing kaafir servants and entrusting them with our homes and children poses a great danger to the morals and religious commitment of the children. 

Shaykh Ibn Baaz (may Allaah have mercy on him) said: 

With regard to employing kaafir women as servants, whether they are Buddhists, Christians or other kinds of kaafirs, is not permissible in this Peninsula, i.e., in the Arabian Peninsula, because the Prophet (peace and blessings of Allaah be upon him) forbade that and urged that the kuffaar be expelled from Arabia, for it is the cradle of Islam and the place where the Message first dawned. So it is not permissible for two religions to co-exist there, and it is not permissible to bring any kaafir there except in cases of necessity as decreed by the authorities, then he (the kaafir) should return to his homeland. End quote. 

Fataawa Ibn Baaz, 6/361 

Shaykh Ibn ‘Uthaymeen said: 

Because a kaafir woman should not remain among you in your house with your family and children, even if the harm is no more than when the family get up to pray and this woman does not pray, the children say: “Why doesn’t this woman pray?” and they love her, so in that case they will think that it is not essential to pray. This is even if she does not teach them her religion, as some people have told us that they heard the servant teaching the children to say that Jesus is God – we ask Allaah to keep us safe and sound. End quote. 

Liqaa’aat al-baab il-Maftoohah, 3/53 

See also questions no. 22980, 26213, 26282, 31242 

Secondly: 

The scholars have stated that it is permissible to take payment for teaching worldly skills, and undoubtedly cooking and food preparation are skills that are very important nowadays. 

It says in al-Mawsoo’ah al-Fiqhiyyah (13/66): 

There is no dispute among the scholars that it is permissible to hire a person to teach permissible skills and professions which have to do with worldly interests, such as sewing, blacksmithing, construction, agriculture, weaving and so on. End quote. 

Thirdly: 

Based on the above, it is permissible according to sharee’ah for your mother to take a payment for teaching the servant different ways of cooking, but she should have told the servant of that before she started to teach her. As for the situation mentioned in the question, the servant has learned how to make food with the encouragement of your mother who chose to do that. She is the one who helped her to do that of her own free will. So it is not permissible for her to take the servant’s notebook in which she has written down what she learned, because it is her property which she has written with her own hand and taken care of. Your mother’s teaching of her was purely voluntary. 

Beware of mistreating her and taking what is rightfully hers, even if she is not Muslim. 

Shaykh Ibn Baaz (may Allaah have mercy on him) said (6/362) to one who brought in a kaafir servant and mistreated her: 

What you and your mother have to do is to send her back to her country. It is not permissible for you or your mother to mistreat her, rather what you must do is treat her in a kind manner while she is with you, until she returns to her country, because Allaah has forbidden wrongdoing to His slaves to mistreat even with regard to kaafirs, as the Prophet (peace and blessings of Allaah be upon him) said: “Beware of wrongdoing, for wrongdoing will be darkness on the Day of Resurrection.” Narrated by Muslim, 2578. And he (peace and blessings of Allaah be upon him) said that Allaah, may He be glorified and exalted, said: “O My slaves, I have forbidden wrongdoing to Myself and I have made it haraam among you, so do not wrong one another.” Narrated by Muslim, 2577. End quote. 

And Allaah knows best.