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, sallAllaahu 'alayhi wa sallam, is His Slave and Messenger.
It is impermissible for you to withhold child support for your daughter simply because her mother would not allow her to visit you abroad. You are not entitled to use child support as a bargaining tool to exercise pressure on her mother because it is an obligation on you to provide for your daughter as long as she is young and has no wealth of her own. Please, refer to Fatwa 163965.
You did the right thing by continuing to pay the fees of your daughter's school. We advise you to reason with your ex-wife and to try reaching a mutual understanding to cooperate in doing what is best for your daughter. Moreover, we advise you to be careful not to let any of these disputes reach your daughter; it is hard enough for her to handle your divorce and be away from her father. If you can travel to visit her, then do so; otherwise, you can communicate with her through the Internet or the phone, especially as you can see her through video calls.
Muslim jurists stated that the parent who has custody of the child does not have the right to prevent the other parent from seeing the child. We have clarified that in Fataawa 125277 and 131338. However, the parent who has custody is not obliged to send the child to the other parent to see him. It was stated in Ad-Durr Al-Mukhtaar, "As-Siraajiyyah reads: 'If the mother is deprived of the right of custody over the child and it is given to the father, he is not obliged to send the child to her; however, she is not prevented from seeing the child." Ibn ‘Aabideen commented on that in his Haashiyah, saying, "Regarding the statement that the father is not obliged to send the child (to visit the mother), the same applies if the situation is reversed, i.e. when the mother is given the right of custody over the child, she is not obliged to send the child to visit the father; however, he is not prevented from seeing the child."
Allaah Knows best.