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 is His slave and Messenger.
If your father had really deserted your wife and does not speak to her, and he has no sound reason for doing so, then he is wrong because it is not permissible for a Muslim to desert his fellow Muslim more than three days except with a sound reason; we have already clarified this in Fataawa 86090 and 84976.
The same thing applies to your mother if she humiliates your wife and hurts her without a valid reason. Both of them are sinful for doing so and they will be questioned about it on the Day of Judgment if they do not repent. Therefore, it is an obligation to advise them and remind them of Allaah.
As regards defending your wife against the injustice that she might experience, then this is something religiously required, but you should do so with gentleness especially that the transgressors are your parents.
As regards the period that a woman needs to rest after giving birth to a child, then it is the specialist doctors who may determine this. Nonetheless, your wife should be wise in dealing with your parents as it appears that there is some jealousy; this often happens between the wife and her mother in-law.
On the other hand, the relationship between you and your parents is a relationship of parentage and kinship and they should keep this relation and not cut ties with you. Also, you are obliged to be kind and dutiful to them, and their mistreatment to you or to your wife should not be a reason for being negligent towards any of them; for more benefit, please refer to Fataawa 87019 and 82254.
With regard to the relationship between your wife and your parents, it is a relationship of in-laws and she does not have any rights on them except the rights that a Muslim has towards another Muslim in general, unless there is a blood relationship between them, in which case, it becomes forbidden to cut ties with them. In addition to this, keeping good relations with the in-laws is something religiously required.
Furthermore, your wife has a right for a separate accommodation without any of your relatives in it, and she is not obliged to dwell with your parents. For more benefit, please refer to Fatwa 84608.
Besides, it is permissible for you to live in a house that is far from your parents if you do not fear that this will affect them adversely, otherwise you may live in an accommodation that is closer to them in order to achieve the two goals together.
Allaah Knows best.