Thank you so much for this service!
I have only one Shabbos/Yom Tov robe or outfit and I make sure it is clean and ready before Yom Tov, but then it usually gets dirty while holding or taking care of the kids. Am I allowed to wash it during chol hamoed so I have something clean to wear for the last days of Yom Tov? If it is allowed, would it be preferable to wash it together with the children’s clothing?
If you only have one garment for Yom Tov, it is permitted to wash it.
You don’t have to wash it together with the children’s garments.
See Shulchan Aruch 534:1 concerning somebody who only has one outfit for Yom Tov, but see Mishnah Berurah (9) who mentions that some authorities are stringent concerning washing garments today. Yet, he is lenient concerning synthetic materials, and other authorities are lenient concerning all clothes (see Yalkut Yosef 534:1).
It is preferable to buy an extra outfit, but there is no obligation to do so, and you can rely on the lenient authorities to wash the garment on Chol HaMoed.
There is no special permit on Chol HaMoed to wash adult clothes together with children’s clothes.