There is a custom that the Havdala wine is not to be shared with the members of the household. It is to be drunk entirely by the one making Havdala.
Women were excluded because some said that the forbidden fruit that Eve gave to Adam, were grapes. This sin caused division and separation. Havdala describes the separation between holy and profane and Israel and the nations. Hinting to Eve’s sin at that time would be inappropriate.
The reason the wine or grape juice should not be shared with the children is that it is necessary to drink a sufficient amount, a רביעית, in order to make the after blessing. If the wine is shared, a sufficient amount will not be consumed.
This information comes from a book titled, טעמי המנהגים, the reason for customs.
This would also imply that women should not make Havdala. This seems to be preferred, but there are times when women need to make Havdala if no men are around. Notice that I prefaced this as a מנהג, a custom.