Learn Portuguese (Portugal): É urgente resgatar a ninhada cuja mãe morreu. - It is urgent to rescue the litter whose mother died.

It agrees with mãe (the mother), not ninhada (the litter). The relative determiner cujo always changes its ending to match the gender and number of the noun that comes immediately after it (the possessed thing). It just so happens that both nouns are feminine singular in this sentence. If we were talking about the litter's father, it would be cujo pai.

Why isn't there a definite article after cuja, like cuja a mãe?

Unlike other possessive words in Portuguese (such as a minha mãe), you must never put a definite article like o or a immediately after any form of cujo. The word cuja does the job of the article all by itself.

Why is resgatar in its infinitive form here? Don't phrases like É urgente trigger the subjunctive?

Expressions like É urgente only trigger the subjunctive when they are followed by the word que and a specific subject (for example, É urgente que nós resgatemos meaning It is urgent that we rescue). Since this sentence makes a general statement without que, we just use the infinitive resgatar (to rescue).

What is the origin of the word ninhada?

ninhada translates to a litter or brood of baby animals. It is built from the root word ninho, which means nest.