The Mishna Berurah in 296:6 says that only the one who makes the havdala should drink because he has to make sure he has enough for a bracha acharona ane if he gives to others, he might not have the correct shiur so it is better off not to give to others. Nowadays our cups are much bigger and hold a lot more than a reviis, according to the Mechaber in 271:14 who says that my kiddush it is mitzva min hamuvchar for everyone to drink, would that apply to havdala and there is a dafka an inyan for others to drink?
Also, from what age should one be careful not give girls to drink from havdala?
You are bringing up an interesting point. The Magen Avrohom 296-4 quotes the Shibolei Haleket that it is the minhag that the person who makes havdalah is the only one to drink from the wine and he doesn’t give anyone else to drink from it. The Mishnah Berura wants to give an explanation, but the minhag still stays the same. Regarding your other point, the Machtzis Hashekel ibid, says that although regarding kiddush it is preferable for those being yotza with the kiddush to drink for the wine, this does not apply to havdalah. He doesn’t explain why.
Being that this is the minhag, little boys and little girls should not drink from the havdalah.