Praise be to Allah.
Undoubtedly this behaviour on your husband’s part is wrong; may Allaah guide him. The husband has no right make such an abhorrent accusation against his wife without proof.
Sowing the seeds of doubt, persisting in them and trying to investigate them are things that lead to destruction of the family. We ask Allaah to keep us safe and sound.
You have to explain to your husband that his thinking is mistaken, and reassure him of your innocence and purity. If necessary you can swear to him that you are innocent, that you love him and that you want to carry on living with him, for he is your husband and the father of your children. You have lived together for a long time, and it should not come to an end just because of some doubts that the shaytaan puts into a person’s mind.
Moreover you know the reason that has made him doubt, which is what he says about you not wanting to be intimate with him. Try to change this idea that he has in his mind. Be loving towards him and draw close to him, and remember that this is something that will raise you in status before Allaah and by which you will attain reward. So do not hesitate to do that and try to find the opportunity to make you husband change his mind, and dispel his doubts by paying attention to him.
Turn to Allaah and ask Him to dispel these doubts and set things straight between you, to guide your husband and to bring you happiness in this world and in the Hereafter.
If you think there is anyone in his family or yours who can advise him and you think that his intervention will be good, then seek his help in dealing with this matter.
We advise you to focus on your worship, for a person may be tested because of his sin, and perhaps you are falling short with regard to the rights of Allaah, may He be exalted. If that is the case, then turn back to Allaah and make up for what you have missed, for if a person sets straight his affairs with Allaah, He will set straight his affairs with other people.
One of the salaf said: If I disobey Allaah, I see that in the attitude of my wife and my mount.
So pray and remember Allaah (dhikr) a great deal, and read Qur’aan at home, especially Soorat al-Baqarah, for a person may be envied (hasad) for what he has of blessings and stability.
We ask Allaah to help and guide you both.
And Allaah knows best.