All perfect praise be to Allaah, The Lord of the Worlds. I testify that there is none worthy of worship except Allaah, and that Muhammad is His slave and Messenger. We ask Allaah to exalt his mention as well as that of his family and all his companions.
The parents are ordained by Allaah to cultivate, discipline and educate their children, and prepare them for the purpose for which they are created. Allaah Says (what means): {O you who have believed, protect yourselves and your families from a Fire whose fuel is people and stones.}[Quran 66:6]. Allaah further Says (what means): {And enjoin the prayer upon your family [and people] and be steadfast therein.}[Quran 20:132]. Furthermore, the Prophet said: "All of you are responsible for the people under your guardianship and everyone of you will be questioned about those under his guardianship. The Imaam (i.e. the Muslim leader) is a guardian and he will be questioned about his guardianship, and a husband is a guardian in his family [wife and children] and he will be questioned about his guardianship, and the wife is a guardian in her husband's home and she will be questioned about her guardianship." [Al-Bukhari and Muslim] For more benefit, please refer to Fataawa 91759 and 89468.
Therefore, if you send your daughters to this non-Muslim female instructor, you are exposing their creed and moral conduct to danger, as it is most likely that your daughters will be emotionally attached to her especially if she treats them well, as a result, they will love her. Consequently, they will try to imitate her in her behaviour and probably in her creed, and then it will be a catastrophe. It is only then that you will regret but it will be already too late.
Hence, you should endeavour to avoid this by taking away your daughters from this place, and remember the saying of the Prophet : ''There is no person whom Allaah makes a guardian over any trust, and he dies while cheating his trust (not fulfilling the rights of the people he is trusted upon), except that Allaah forbids paradise for him.'' [Al-Bukhari and Muslim] In addition to this, there is no necessity in teaching your daughters how to swim.
As regards the non-Muslims who do not cover themselves properly and dress scantily, then this is not a sound reason for doing what would cause Allaah's Anger. Indeed, due to the widespread evil and acts of disobedience which happen in the non-Muslim countries, the scholars stated that a Muslim should not reside there except for a necessity or a dire need.
For more benefit, please refer to Fataawa 83365 and 81642.
Allaah Knows best.