I sort of agree. The cousin was interested in your husband. Just because he is now married to you, it doesn’t necessarily mean that she’ll stop liking him. Ever heard of the scorned woman’s revenge? It’s fine if you trust your husband, and if he’s being honest with you, even better. But something just seems wrong about the cousin texting late at night and that much… I’m not trying to make you paranoid… I mean there are people who send thousands of texts and find it normal. This behavior that you find abnormal could be completely normal to the cousin. Just be cautious of her.
How to rebuild the trust… now that you know a little more about the cousin and her problems, try to stay open with your husband about it. Don’t make it seem like you hate his cousin. Try to be objective and offer advice to your husband on how to deal with the cousin and her issues.