Is it permissible for a husband to ask his wife to speak with her children in a language that the other wife does not understand, given that English is the common language between them?

It is forbidden for two people to whisper together to the exclusion of a third when there are three present. This prohibition may also extend to speaking in a language the third person does not understand, because that would sadden him. However, if there are more than three people, there is no harm in two of them whispering to the exclusion of the others. The prohibition applies when the third person is present from the beginning. But if he arrives after the whispering has begun, there is no harm for them to continue, though it is incumbent upon him not to join them unless they give him permission. The prohibition here is one of tahrim (absolute prohibition).