Learn English – the relation of the brother’s wife’s nieces to me

Once you are married to anyone, you immediately assume the titles which the different relatives have to address you with. Remember, you have to get married before you get these title(i.e. you're not a brother-in-law, unless you are married and then by law you are a brother, although not a blood-brother).

It is not necessary that your marriage pre-date the birth of any of your 'gained' relatives. For example, your step-son will call you step-father even if he was born before you married his mother.

They are your cousins' cousins.

An English-speaking person wouldn't confuse this for a simpler relationship for which a single word or fixed phrase existed because (except where we want to avoid an ambiguity) we tend to select a formulaic word or phrase in preference to a less formulaic one for family relationships. In support of this, consider "brother" vs. "parents' son". "brother in law" vs. "wife's brother", etc. Thus if we see an unformulaic phrase like "cousins' cousin" we would guess it wasn't a circumlocution that referred to a cousin or sister or anything else that it could technically be.