having a long history of affinity with green anarchist thought, i kinda like the word "domestication", so far as i understand it. i think it is one of the less ambiguous words used by folks critical of civilization, at least at a broad level. however, outside of anti-civ circles, the use of the term often does not include humans. which for me is definitely problematic. virtually all modern humans are domesticated, to some degree or another.
as for the general treatment of children and non-human animals, in the context described in the question, i feel like that is more related to the concept of charity and (as rs666 mentioned) "helping the weak". while domestication is a large part of what makes children/non-human animals (as well as adult human animals) seen as "weak", i'm not sure what the relationship is between the two (domestication and charity/helping the weak). i'm also not sure about the relationship between those seen as "weak" and those seen as incapable of "speaking for themselves".
as for speaking for oneself, i'd say that is way too generally applied. most children i've known that are older than 2 or so can surely express themselves, at least in terms of what they like/want vs not. even non-human animals have ways of expressing their needs and desires (especially related to humans), and an individual that has any kind of connection with them will typically be able to read those expressions, more or less. communication is not nearly as limited as most humans seem to think it is (and most humans are far worse at it than they think they are, myself obviously included).
and what about non-animal life? plants have been domesticated for as long as animals (human and non) have, and they can't "speak for themselves". i know most people consider any life without a human-detectable central nervous system to be biologically incapable of things like fear, desire, pain, love, joy, etc. and of course that comes from science(tm), so fact it is. i make no such assumptions. and honestly, that is the logic used by ideological vegans to "prove" that their mode of food consumption is "good", and all others are "bad". (just as anti-vegans use science to "prove" their own eating habits are the correct ones).
"helping the weak" really seems to be the crux of this question, and to me it seems largely separate from the issue of domestication. to me that is more a matter of ideology and relationships.
charity is a capitalist, classist, hierarchichal, non-mutualistic construct. numerous ideologies employ it as part of their package (liberalism, progressivism, many forms of religionism, capitalism, etc). so it should be easy for anarchists to reject it, imo.
i think that like anything else, "helping the weak" needs to be seen within the context of a given situation. as an ideology, fuck that shit. as a personal response to a situation that one is close to, i may well intervene if it seems appropriate given my understanding of the situation and those involved (human and otherwise). that is really no different than how i would treat any situation. the situation may include a being that is less capable, in some relevant way, than the other(s). that is nothing more than additional context to be considered.
[maybe this should be a comment?]