Looking for translations of room for children I found the word "brattery" along with the word "nursery", which I believe is most commonly used for children's room in a house. Is "brattery" still in use or is it obsolete now? Or does it have some specific context?
Brat is a word originating c.1500, slang meaning beggar's child (Etymonline)
According to Encyclo.Co.UK, a brattery is British slang for a nursery, a creche, a school.
A Dictionary of Slang and Unconventional English lists its use from c. 1780 as a pejorative colloquialism for nursery
The apartment above my head proves a squalling brattery. - Beckford, 1834
A recent use:
In a recent display of full-blown brattery, several liberal operatives renewed attacks on me at another website. - The BulletProof Monk
Though I've never heard it, seeing as brat and rug rat are common names for small children, I think it's meaning is easy to arrive at.
If you saw it used recently, it's simply a humorous addition of "-ery" to the word "brat".
Note that we have common ("real") words like nunnery, fishery and so on.
It's somewhat common to do the same thing to other words - for humorous effect.
So, say you refer to your buddies as "wankers", you might walk in and say "what's happening in this wankery today!" ... ok?
It's just possible that the word, in the distant past, existed and was used: but it does not today.
(1) It is "not a word", do not use it ever.
(2) Adding "-ery" is a somewhat common sort of language humour. That's what you saw, if you saw or heard a recent usage.
Note - you have mentioned in a comment (why not edit the question?) this is from a Russian to English dictionary. Forget it, the dictionary is crap.
That's all there is to it.
Just to be perfectly clear Mikhail, if you don't know, "brat" is simply current aggressive slang for "badly behaved kid". (Don't use it when talking normally; only use it when screaming or about to get in a fight. Example "Control that brat of yours!")
It's about the same tone as calling an adult an "idiot".