Is it permissible to interrupt the prayer if a child's crying distracts the worshippers, and what is the ruling on completing it if the sound of loudspeakers drowns out his crying?

You did well not to interrupt your prayer because of the child's crying. It is not permissible to interrupt an obligatory prayer except for a legitimate Shar'i excuse, and a child's crying is not an excuse that permits interrupting it. Your inference that the women of the Companions did not interrupt their prayers due to a child's crying is a correct inference. We advise you to mend your relationship with your husband and not to retaliate in kind.