All perfect praise be to Allaah, The Lord of the Worlds. I testify that there is none worthy of worship except Allaah, and that Muhammad is His slave and Messenger.
First of all, we ask Allaah to facilitate your matter, to make a way out to your difficulties and to rectify your husband’s affairs.
It is Islamicly not permissible for a man to have an affectionate relationship with a non-Mahram woman because this is the conduct of the people of the pre-Islamic era of ignorance, and Allaah forbade it as He Says (what means): {…or taking [secret] lovers.}[Quran 5:5]
Therefore, your husband is obliged to cut any relationship with this woman and it is not permissible for him to keep in touch with her even through the Islamic messages that he mentioned, as the devil may make this as a means to commit what is Islamicly forbidden. The fact that she is already married confirms that he should avoid her.
Moreover, he should be very firm with this woman in not sending him messages, and if she insists, he may change his phone number.
However, you should not investigate whether or not your husband is still in relationship with this woman. Nonetheless, since what happened has already taken place, then we advise you to be patient and try to solve the matter with your husband with wisdom while being keen on not causing any dissension because of this matter. We also advise you to care of your husband even more and beautify yourself to him as this increases the affection and love between both of you, and so that he would not be attracted to another woman.
Allaah Knows best.