Praise be to Allah.
There is no sin on the women in this situation if she delays Hajj until a later year, firstly because many scholars say that it is not obligatory to do Hajj straight away and a person may delay it even though he is able for it. Secondly, this woman needs to stay in order to look after her children, and taking care of children is very important. The Prophet (peace and blessings of Allah be upon him) said: “A woman is a shepherd in her husband’s house and is responsible for her flock.” So I say that she may wait until next year. We ask Allah to make things easy for her, and to enable her to do all that is good. End quote.