First of all, we ask Allaah to reward you with good for your keenness to avoid following the ways of the disbelievers, and your fear of imitating them. This is how the believer is; he is proud of his faith and his Islam, and he does not agree to be a blind follower of those with whom Allaah is angry among the Jews and Christians.
But there is nothing wrong with what your wife and her sisters are doing, as it seems to us. It is not the haraam kind of imitation, in sha Allaah, because setting aside Saturday for visits is not because it is a special day, rather it is because this is easier for them and is more suited to the family’s circumstances, as it is possible for everyone, because of this day off, to visit. Shaykh al-Islam Ibn Taymiyah (may Allaah have mercy on him) said:
With regard to the one who does something and it so happens that others do it too, and one of them did not copy the other, then the question of whether this is an imitation or not is subject to further discussion. End quote.
Iqtida’ al-Siraat al-Mustaqeem (p. 82)
He also said:
That which is not originally taken from them, but they do it too, does not come under the prohibition on imitating them, but it may mean missing out on the benefits of being different. Whether it is makrooh or haraam depends on shar’i evidence as to whether it is imitating them, because we cannot say that we are imitating them, rather it may be said that they are imitating us. End quote.
Iqtida’ al-Siraat al-Mustaqeem (p. 223)
From the words of Ibn Taymiyah quoted above about the guidelines on what is the haraam kind of imitation or resemblance, it may be understood that your wife and her sisters setting aside Saturday for their visits is not haraam according to sharee’ah, for several reasons:
1. Visiting relatives is prescribed in our religion at all times, and it is the practice of our Prophet (peace and blessings of Allaah be upon him) and of our righteous forbears at all times and in all places. There is nothing wrong with singling any day out for that, according to circumstances and time. This is according to scholarly consensus.
2. Visiting people on Saturdays is not one of the unique characteristics of the Jews and Christians, and it is not something that has been adopted from them. Rather it is something that all people have in common, and is not unique to one nation rather than another. Rather what is unique to the Jews is taking Saturday as a holy day on which the people show the outward manifestations of it being a holy day, that they do not do on other days.
As it does not seem that this action of theirs is imitation of the kuffaar, and there is no fear that they may do that, then there is nothing wrong with their singling out Saturdays for such visits, if that is easiest for them and most suited to their circumstances.
Al-Bukhaari (1193) and Muslim (1399) narrated from ‘Abd-Allaah ibn Dinar that Ibn ‘Umar (may Allaah be pleased with him) used to go to Quba’ every Saturday and he used to say: I saw the Messenger of Allaah (peace and blessings of Allaah be upon him) coming to it every Saturday.
To sum up: If singling out Saturdays for visits is easier for them, then there is nothing wrong with it, in sha Allaah, and it does not seem that there is anything wrong with it. If their circumstances allow them to choose another day, other than Saturday or Sunday, or they can switch it every time, that is more on the safe side for them and further removed from imitation of the kuffaar, and is more obviously being different from the kuffaar in their festivals and special days.
And Allaah knows best.