The woman(1) and its husband went shopping, and it bought a pair of new pants.

We already have an equally confusing type of sentence, with no contrived pronoun-switching:

The woman and her sister went shopping, and she bought a new pair of pants.

Who did? (Probably "the woman".) We can usually manage to work it out when we actually use such a sentence in real life.

Having gender-specific pronouns in English only helps in some cases. Anyway, Turkish has the non-gender specific pronoun thing - only "it" - no "he" or "she". So I've become used to my Turkish friend referring to her mother as "he" and her husband as "she" occasionally - it breaks the flow when she stops to think about the pronoun - and I know her well enough to interpolate the errors. I am inclined to see her side of the argument...the "he" and "she" don't necessarily clear things up all the time! Try going to an all-girls' school! All your stories degenerate into "her" and "she", with much extra clarification needed.