score:3
Yazid went by the standards of the day, but went about them in a somewhat twisted way. Women and children were off-limits for killing, but anyone who took up arms against him was killed. Husayn was holding his six-month-old son in a gesture of peacemaking, but both were killed when he approached Yazid's army. Likewise, while they spared Ali ibn Husayn Zayn al-Abidin because Zaynab bint Ali used herself as a human shield, they carried Zaynab off in chains sans-veil for her insolence.
So yes, Yazid had the interest of removing the threat of Husayn's group, but still (for the most part) held to the tradition of sparing women and children. This meant that other than the six-month-old (who may have been in the line of fire if his father was carrying him towards the opposing army), Yazid held to the letter of the law. Now, did he do so from religious belief, or so that the people of Kufa's tenuous support for Ubayd Allah ibn Ziyad didn't fail? Maybe a mix of both? It's hard to say.