Entries linking to childish
Old English cild "fetus, infant, unborn or newly born person," from Proto-Germanic *kiltham (source also of Gothic kilþei "womb," inkilþo "pregnant;" Danish kuld "children of the same marriage;" Old Swedish kulder "litter;" Old English cildhama "womb," lit. "child-home"); no certain cognates outside Germanic. "App[arently] originally always used in relation to the mother as the 'fruit of the womb'" [Buck]. Also in late Old English, "a youth of gentle birth" (archaic, usually written childe). In 16c.-17c. especially "girl child."
The wider sense "young person before the onset of puberty" developed in late Old English. Phrase with child "pregnant" (late 12c.) retains the original sense. The sense extension from "infant" to "child" also is found in French enfant, Latin infans. Meaning "one's own child; offspring of parents" is from late 12c. (the Old English word was bearn; see bairn). Figurative use from late 14c. Most Indo-European languages use the same word for "a child" and "one's child," though there are exceptions (such as Latin liberi/pueri).
The difficulty with the plural began in Old English, where the nominative plural was at first cild, identical with the singular, then c.975 a plural form cildru (genitive cildra) arose, probably for clarity's sake, only to be re-pluraled late 12c. as children, which is thus a double plural. Middle English plural cildre survives in Lancashire dialect childer and in Childermas.
Child abuse is attested by 1963; child-molester from 1950. Child care is from 1915. Child's play, figurative of something easy, is in Chaucer (late 14c.):
I warne yow wel, it is no childes pley To take a wyf withouten auysement. ["Merchant's Tale"]
The -ish in verbs (abolish, establish, finish, punish, etc.) is a mere terminal relic from the Old French present participle.