Should she end her relationship with some kaafir women or use the opportunity for da’wah?

Praise be to Allah.

Firstly: 

It is not permissible for a Muslim man or woman to take a male or female friend who is not a Muslim, because Allah has forbidden us to love the kuffaar or take them as close friends and companions, as He says: 

{لَا تَجِدُ قَوْمًۭا يُؤْمِنُونَ بِٱللَّهِ وَٱلْيَوْمِ ٱلْءَاخِرِ يُوَآدُّونَ مَنْ حَآدَّ ٱللَّهَ وَرَسُولَهُۥ وَلَوْ كَانُوٓا۟ ءَابَآءَهُمْ أَوْ أَبْنَآءَهُمْ أَوْ إِخْوَ‌ ٰنَهُمْ أَوْ عَشِيرَتَهُمْ ۚ أُو۟لَـٰٓئِكَ كَتَبَ فِى قُلُوبِهِمُ ٱلْإِيمَـٰنَ وَأَيَّدَهُم بِرُوحٍۢ مِّنْهُ ۖ وَيُدْخِلُهُمْ جَنَّـٰتٍۢ تَجْرِى مِن تَحْتِهَا ٱلْأَنْهَـٰرُ خَـٰلِدِينَ فِيهَا ۚ رَضِىَ ٱللَّهُ عَنْهُمْ وَرَضُوا۟ عَنْهُ ۚ أُو۟لَـٰٓئِكَ حِزْبُ ٱللَّهِ ۚ أَلَآ إِنَّ حِزْبَ ٱللَّهِ هُمُ ٱلْمُفْلِحُونَ}

'Translation' {You (O Muhammad) will not find any people who believe in Allah and the Last Day, making friendship with those who oppose Allah 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). Allah is pleased with them, and they with Him. They are the party of Allah. Verily, it is the party of Allah that will be the successful} [al-Mujaadilah:22]. 

{يَـٰٓأَيُّهَا ٱلَّذِينَ ءَامَنُوا۟ لَا تَتَّخِذُوا۟ ٱلْيَهُودَ وَٱلنَّصَـٰرَىٰٓ أَوْلِيَآءَ ۘ بَعْضُهُمْ أَوْلِيَآءُ بَعْضٍۢ ۚ وَمَن يَتَوَلَّهُم مِّنكُمْ فَإِنَّهُۥ مِنْهُمْ ۗ إِنَّ ٱللَّهَ لَا يَهْدِى ٱلْقَوْمَ ٱلظَّـٰلِمِينَ}  

'Translation' {O you who believe! Take not the Jews and the Christians as Awliyaa’ (friends, protectors, helpers), they are but Awliyaa’ of each other. And if any amongst you takes them (as Awliyaa’), then surely, he is one of them. Verily, Allah guides not those people who are the Zaalimoon (polytheists and wrongdoers and unjust)} [al-Maa’idah:51]. 

{يَـٰٓأَيُّهَا ٱلَّذِينَ ءَامَنُوا۟ لَا تَتَّخِذُوا۟ بِطَانَةًۭ مِّن دُونِكُمْ لَا يَأْلُونَكُمْ خَبَالًۭا وَدُّوا۟ مَا عَنِتُّمْ قَدْ بَدَتِ ٱلْبَغْضَآءُ مِنْ أَفْوَ‌ ٰهِهِمْ وَمَا تُخْفِى صُدُورُهُمْ أَكْبَرُ ۚ قَدْ بَيَّنَّا لَكُمُ ٱلْءَايَـٰتِ ۖ إِن كُنتُمْ تَعْقِلُونَ}

'Translation' {O you who believe! Take not as (your) Bitaanah (advisors, consultants, protectors, helpers, friends) those outside your religion (pagans, Jews, Christians, and hypocrites) since they will not fail to do their best to corrupt you. They desire to harm you severely. Hatred has already appeared from their mouths, but what their breasts conceal is far worse. Indeed We have made plain to you the Ayaat (proofs, evidences, verses) if you understand} [Aal 'Imraan:118]. 

Secondly: 

It is permissible for a Muslim to correspond with them and to give them gifts, with the aim of calling them to Islam and showing them its beauty, subject to the condition that he has sufficient knowledge and faith which will enable him to call them and protect him against the specious arguments and devious methods of the people. But the one who is not equipped to do so should not involve himself in this field, because of the temptations to which he may be exposed, or the doubts with which he may be faced and be unable to refute, in which case it would lead to his going astray and being doomed- Allah forbid. 

Thirdly: 

If this correspondence is limited to the exchange of sewing ideas and benefiting from them in this way, without it involving loving them, regarding them as friends, congratulating them on their festivals etc, then there is nothing wrong with it in sha Allah. The Prophet (peace and blessings of Allah be upon him) used to interact with the Jews, buying and selling. 

There is nothing wrong with giving gifts to them, subject to the condition that they are not in a state of war against Islam and the Muslims. Allah says:

  {لَّا يَنْهَىٰكُمُ ٱللَّهُ عَنِ ٱلَّذِينَ لَمْ يُقَـٰتِلُوكُمْ فِى ٱلدِّينِ وَلَمْ يُخْرِجُوكُم مِّن دِيَـٰرِكُمْ أَن تَبَرُّوهُمْ وَتُقْسِطُوٓا۟ إِلَيْهِمْ ۚ إِنَّ ٱللَّهَ يُحِبُّ ٱلْمُقْسِطِينَ}

'Translation' {Allah does not forbid you to deal justly and kindly with those who fought not against you on account of religion nor drove you out of your homes. Verily, Allah loves those who deal with equity} [al-Mumtahanah:8].

al-Sa'di (may Allah have mercy on him) said p. [1016]: "i.e., Allah does not forbid kindness, upholding of ties and good and fair treatment of mushrikeen among your relatives and others, so long as they are not fighting against you on account of religion or driving you out of your homes. There is no sin in upholding ties with them, because there is nothing wrong with upholding ties with them in this case (End quote). 

Fourthly: 

The means of calling people to Islam are many and various, such as the following: 

1. Direct discussion, in which we should focus on the merits of Islam, the truth of Tawheed, the importance of faith, the truthfulness of the message of Muhammad (peace and blessings of Allah be upon him), and then explain the falseness of other religions and the distortions and alterations that have befallen them.

2. Giving books and pamphlets which speak of Islam and encourage people to enter into it.

3. Directing others to sites which explain Islam and call people to it, and answer the specious arguments of those who oppose it, and debate with them in the manner that is better. 

The one who calls others to Islam must be equipped with Islamic knowledge and strong faith, so that he may resist specious arguments and temptations. Otherwise he should leave this field to others, and fear Allah with regard to himself and not expose himself to things that may lead to doom. The Muslim should beware of letting any love for the kaafir enter his heart. 

And Allah knows best.