These are general laws related to Jewish holidays and the intermediate days of Pesach and Sukkos.

YOM TOV & CHOL HAMOED
A. REJOICING YOM TOV

1. Jews are obligated within Torah Law to rejoice on Yom Tov. The head of a household is required to ensure that all members of his householdparticpate in the mitzvah of rejoicing on Yom Tov. The Gemara saysthat the father should buy candies and other treats for his children

and the Shulchan Aruch codifies this as a binding halacha today. [1] B. HAIRCUTTING ON CHOL HAMOED
1. The intermediate days of Pesach and Sukkos are called Chol Hamoed. The laws of Chol Hamoed are complex [2] and we will only address thechinuch laws relating to Hair Cutting and Laundry.

2. Haircutting is generally prohibited on Chol Hamoed, however, under cases of distress and discomfort, such as when the hair is very longand bothersome, parents may cut their childrens’ hair during Chol HaMoed.This only applies to children under Bar/Bas Mitzvah age. [1][2]

3. If a boy’s 3rd birthday (upsheren) falls on Chol Hamoed, he may have his first haircut on that day. [2]

 

C. LAUNDRY ON CHOL HAMOED
1. Laundry is also generally prohibited on Chol Hamoed, however, children’s laundry is permitted under certain circumstances. [1][2]

2. Cloth diapers and other infant’s clothing are not included in thisruling. [1]

2. Non-infant children’s clothes should be laundered before Yom Tov, however, since children frequently soil their clothing, and if their cleanlaundry is depleted during the festival, their soiled clothes can bewashed. [2]

3. One is permitted to wash a child’s soiled article of clothing even if there is another clean outfit to wear, provided the clean outfit is notas appropriate for the holiday as the dirty one. [2]

4. Washing is permitted at the point during Chol Hamoed when a particular item of the child’s clothing becomes available. [2]

5. Once such washing is permitted, any of the child’s other clothingthat will be needed for the remainder of the festival, even if they are not needed immediately, may be washed. [2]

6. The clothing of infants together with older small children may bewashed together in one batch on Chol Hamoed. [1] Garments that are not needed may not be added to the wash. [1][2]

D. REFERENCES

[1] A Parent’s Guide to Teaching Children Mitzvot by Rabbi Shmuel Singer

[2] Children In Halachah by Rabbi Simcha Bunim Cohen.