Praise be to Allah.
If you have already done the obligatory Hajj, then you have the choice with regard to a voluntary Hajj between doing it this year or delaying it until next year, because of what you mentioned about being busy with your family or wanting to stay with them and so on. In that case you can choose not to do it at all, because it is voluntary and not obligatory.
But if the question is about the obligatory Hajj, then it depends. There are two scholarly views, one of which is when one becomes able to afford it, Hajj becomes obligatory and must be performed in the same year; the other view says that it may be delayed. However, the more correct view is that it becomes obligatory with immediate effect and must be performed in the same year. The one who can afford provisions and a means of transportation is obliged to do Hajj, and it is not permissible for him to delay it. Please see question no. 41702
Based on that, if your leaving your wife will not cause her or the child any harm, then you must do Hajj this year and you do not have the option of delaying it in the hope that your family could go with you. But if your wife has enough money to do Hajj, or you can pay the expenses of Hajj for her, and it will not harm her or her baby if she goes to Hajj, or she can leave the baby with someone who can look after him, then she is obliged to go for Hajj. Otherwise, it is permissible for her to delay it.
The point is that Hajj may be obligatory for the husband but not for the wife, depending on whether the conditions are met or there are any impediments. So the husband should not delay his obligatory Hajj because of wanting to take his wife with him for Hajj.
Shaykh Ibn ‘Uthaymeen (may Allah have mercy on him) was asked the following question: My wife has not yet done the obligatory Hajj, and we have a baby who is four months old and he is being breastfed by his mother. Should she do Hajj or stay with her baby? And is it better, if she goes for Hajj, to take pills in order to stop menses, or not? Please advise us, may Allah bless you.
He replied: If the baby will not be affected or harmed by her leaving him, in that he can be breastfed by someone other than his mother, and there is someone who can look after him properly, then there is nothing wrong with her doing Hajj, especially if it is the obligatory Hajj. But if there is any fear for the child, then it is not permissible for her to do Hajj even if it is the obligatory Hajj, because the breastfeeding mother is permitted to not observe the obligatory fast if she fears for her child. So how can it not be permissible for her to postpone Hajj if she fears for her child? If she fears for her child, then what she must do is stay, then when he is older she can do Hajj next year. There is no blame on her if she stays home and does not do Hajj, because in this case she is not obliged to do Hajj immediately.
With regard to using pills during Hajj or ‘Umrah, there is nothing wrong with that, because this is a need. But it is essential to consult a doctor, because the pills may be harmful and may cause her harm.
End quote from al-Liqa’ ash-Shahri, 10/25
And Allah knows best.