Is it permissible for me to take my children from my Muslim ex-wife, who is married to a Christian man, fearing for them the Western dissolution, and in order to raise them according to Arab principles and the Islamic religion in my country?

If the mother is immoral, her right to custody is forfeited, and custody transfers to the next eligible person. If there is no one more entitled to custody than you, or if there is someone but they are unfit for custody or have relinquished it, then custody transfers to you. If you fear for your children's loss, deviation, or the immorality of the custodian, then you have the right to claim them. And if you intend to travel a journey of relocation, then you have a greater right to your children, as mentioned by the esteemed scholar Ar-Ramli, may Allah have mercy on him.