Praise be to Allah.
The believer should think well of others, assume the best and keep away from doubt and suspicion that have no basis, because Allah says (interpretation of the meaning): “O you who believe! Avoid much suspicion; indeed some suspicions are sins. And spy not” [al-Hujuraat 49:12].
This Qur’aanic etiquette is one of the means of peace of mind, happiness and comfort, because suspicion prompts one to search and try to find out, and it may lead to spying, and that is usually accompanied by worry, anxiety and distress.
But if there are things that call for doubt and suspicion, the husband has to try to remedy the matter and set things straight, and to block the ways that may lead to fitnah and evil. If the wife -- for example -- gets in touch with people or corresponds with them or is away from the house without any convincing reason and the like, then he may prevent her from doing that. If he is worried about her staying on her own in the house, he can bring her to live near his family or righteous neighbours.
We have previously discussed the ruling on setting up recording devices to keep an eye on family conversations. See the answer to question number 13318.
And Allah knows best.