gender-neutral words we lack in English

So it's interesting to me that although we mostly don't have grammatical gender in English, we do have some words with inherent gender but no neutral alternative (which other gendered words do have). Viz:

mother, father, parent
sister, brother, sibling
daughter, son, child

But:

niece, nephew, _____
aunt, uncle, _____

And, interestingly, _____, _____, cousin.

I wonder why we can have gender-neutral terms for the immediate family but not for the slightly extended one. Bit of a drag.

I was going to use animal terms here, too, which is also interesting:
mare, stallion, horse
filly, colt, foal
cow, bull, _____ (cattle, sure, but that's a mass rather than a count noun; you can't specify one gender-neutral adult animal, and maybe not juveniles either - is it heifer, calf, _____ or heifer, _____, calf?)
ewe, ram, sheep
_____, _____, lamb
?nanny, billy, goat? (can you say "a nanny" or does it have to be "a nanny goat"?)
_____, _____, kid
?bitch, dog, _____? (rarely used anymore, of course, and/so people would probably correct me to bitch, _____, dog if they're prepared to use "bitch" in the canine sense at all)
_____, _____, pup
_____, _____, wolf
?vixen, _____, fox?
?_____, tom, cat?
_____, _____, kitten
hen, cock, bird/fowl (is this true of all birds and just generally not used for most of the little flying ones?)
_____, _____, chick
?jenny, mule, _____? (or jenny, ____, mule?)
sow, hog, pig
_____, _____, piglet
... we don't give a shit about the genders of fish, do we.