Havdala during the nine days:
When saying Havdala during the nine days [Motzei Shabbos Chazon] one is to give the wine to a child to drink [whether male or female, although some rule only male] which has reached the age of Chinuch [of blessings although some say also Chinuch of Havdala] but has not yet reached the age of Chinuch for mourning. If such a child is not available he may drink the Havdala wine himself as usual.
Havdala when Tishe Beav falls on Motzei Shabbos: 
In the event that Tishe Beav falls on Motzei Shabbos, Havdala over wine is recited on Motzei Tishe Beav, which is Sunday night. The blessings of Besamim and Haeish are omitted from Havdala. One is to say the blessings of Meorei Haeish on Motzei Shabbos upon seeing a candle. The blessing of Besamim is not said at all, not on Motzei Shabbos or Sunday night.
The Nusach of Havdala: On Sunday night one begins Havdala from “Hinei Keil Yeshuasi”.
Eating and drinking: It is forbidden to eat and drink after Tishe Beav until one says Havdala over wine, just as is the law on Motzei Shabbos. It is permitted to drink water although our custom is to avoid doing so.
Who is to drink the Havdala wine in the above scenario?
Some Poskim rule one may drink the wine of Havdala himself. There is no need to give it to a child to drink. Others however rule wine should not be used, unless it is given to a child, just like on Motzei Shabbos Chazon.
 Rama 551/10
Other Opinions: Aruch Hashulchan 551/26 rules one is not to say Havdala over wine but rather over beer although some are accustomed to drink wine. Kaf Hachaim 551/152 says Sefardim have the custom to drink the Havdala wine themselves. However by Birchas Hamazon they do as the Rama.
 Based on 190/4
 Based on 295/4 that only one who fulfills their Havdala obligation may drink the wine, and women and girls are disputed in whether they are obligated in Havdala.
 Based on 190/4
 Kitzur Halachos 295 footnote 5 based on 295/4 that only one who fulfills their Havdala obligation may drink the wine.
 M”A 551/31. This means the child is not yet old enough to understand the mourning period.
 Michaber 556/1
 So writes Hiskashrus 940 footnote 82 to be custom of the Rebbe. This dispute seemingly follows the same dispute regarding if these versus are to be recited on Motzei Yom Tov.
Other Opinions: In Luach Kolel Chabad it states one is to say Havdala like the order of the rest of Jewry which is to skip the verses of Hinei Keil Yeshuasiy.
 M”B 556/3 in name of Degul Merivava; Piskeiy Teshuvos 558/3
 Peri Megadim 556 A”A 2; Aruch Hashulchan 556/2; Luach Eretz Yisrael of Harav Tukachinsky