In a previous question you wrote: Even an Ashkenazi with a previous custom to observe Sphira until Shavuot may make a wedding earlier when it is a widower with small children. In general Rav Moshe was very lenient about changing from one custom of sephira to another, and attending weddings against one’s own custom if it is the custom of the bride and groom. How does making a wedding relate to being a widow in this case?

The Halacha usually refers to cases of widowers with small children as a reason to forgo certain rules of mourning that would restrict marriage, because it is assumed that the children require a mother. The same logic would work if a widow has small children and she feels they require a father for their care. There may be other situations where an early marriage is a necessity. Certainly a Halachic authority should be consulted in each case.