What is the ruling regarding the maintenance of children if the father returns to his home country, while the wife refuses to return, and the father is unable to provide for them due to the difference in wage levels?

You have made an excellent decision to return to your Muslim country. Your wife must move with you if you request it. If she refuses and a divorce occurs, custody belongs to the father if one of the parents moves to a new location for permanent residence. This is the view of the Four Imams. The children's maintenance is obligatory upon you to the extent of their sufficiency or your capacity if you are unable to provide more. If the wife disobeys, the husband may refrain from divorcing her until she ransoms herself from him, and he can make her ransom her undertaking the children's maintenance.