You are not allowed to put any pressure on your wife to visit your parents.
And she has no duty to do so nor will she commit any sin by her rejection. But if she accepted to do so she will be rewarded.
As for your statement that she must follow the orders of her husband this is not a blueprint, in fact scholars counted 3 limitations among them as one my read:
In the following I'll translate from Arabic language, as the translation is of my own take it carefully!
ابن نجيم: المرأة لا يجب عليها طاعة الزوج في كل ما يأمر به؛ إنما ذلك فيما يرجع إلى النكاح وتوابعه خصوصا إذا كان في أمره إضرارا بها. انتهى.
Ibn Najim (Hanafi scholar) said: A woman is not obligated to obey her husband in everything he orders. Rather, that is with regard to marriage and its consequences, especially if it is harmful to them. End quote (Source)
As they are not part of her family or relatives that are considered under the Arabic definition of the term:
Which is the kind of kinship ordered to tie the bond with and referred to in many ahadith like in the Sahih hadith:
"Whoever believes in Allah and the Last Day, should serve his guest generously; and whoever believes in Allah and the Last Day, should unite the bond of kinship (i.e. keep good relation with his kith and kin); and whoever believes in Allah and the Last Day, should talk what is good or keep quiet." (Sahih al-Bukhari)
So if you put pressure on her to do so you might be sinning, while she is permitted not to follow such an order if made.
Who are the kinship which falls under the term of Rahim?
The scholars have different opinions on this, but none of them counted the family of the husband among those -from the perspective of his wife-! As the term is mainly related to relatives from either mother's or father's side, so as far as there's no blood relationship between husband and wife this doesn't apply to any member of his family.
In the fatwa islamqa #75057 you may find the different opinions of scholars:
The scholars differed as to the definition of the kindred with whom ties of kinship must be upheld. There are three views:
1-That it means one’s mahrams (those whom one is forbidden to marry)
2-That it means those who will inherit from you
3-That it means all blood relatives, whether they are heirs or not.
The correct scholarly view is the third one, that it refers to all blood relatives – not relatives through breastfeeding – on both the father’s side and the mother’s.
The family of the husband are neither mahrams of the wife (at least none of them is so by default before the marriage, as said airliner Rahim is in first place about blood relatives), nor will they inherit from her nor are they among her blood relatives.
The following is rather off topic, but well-meant advise
How it should be
However it is better if you could convince your wife to visit your family and vice versa because it is an abuse towards them. And if possible each of you should talk to both sides, your wife and your parents and if necessary your wife should talk to her parents kindly and remind them the words of Allah:
And not equal are the good deed and the bad. Repel [evil] by that [deed] which is better; and thereupon the one whom between you and him is enmity [will become] as though he was a devoted friend. (41:34)
And also have in mind the hadith saying:
Allah's Messenger, I have relatives with whom I try, to have close relationship, but they sever (this relation). I treat them well, but they treat me ill. I am sweet to them but they are harsh towards me. Upon this he (the Holy Prophet) said: If it is so as you say, then you in fact throw hot ashes (upon their faces) and there would always remain with you on behalf of Allah (an Angel to support you) who would keep you dominant over them so long as you adhere to this (path of righteousness). (Sahih Muslim)
which recommends visiting people and holding up ties of kinship with people who dislike you.
And remember that your children are/will be part of both families, therefore it would be best if both of you have at least a regardful relationship towards the families of each of you. As else the poison which this kind of rejection cause may grow and split your marriage by poisoning your children.
See also the following fatwas:
- islamqa #1426 on rulings on upholding ties of kinship for women.
- islamweb #408067 -in Arabic- on the ruling whether husband has the right to order or put pressure on his wife to make her visit his parents. And that her refusal is not a reason for talaq. A similar fatwa #220000 and islamqa #154607 - both in Arabic-.
- islamqa #101321 "If her husband prevents her from visiting her parents, will she be rewarded for her intention?".