Does the wife's seeking refuge with her psychologically ill sister-in-law without her husband's knowledge diminish the reward for her patience, and is wishing for death incompatible with patience?

The default rule is that complaining to people is forbidden, but certain cases are exempted, such as intending to offer advice or prevent harm. In this case, you are permitted to complain to your husband's sister, and it is permissible to use tawriyah (double entendre) to conceal the matter from him. However, if there is no benefit, it is not permissible, especially given your husband's dislike.

As for complaining that involves discontent with Allah's decrees, it is forbidden. However, informing a friend or relative about one's situation is not blameworthy, but the reward for one who conceals it is greater.

As for wishing for death, it is disliked if it is due to worldly harm, but it is permissible if it is out of fear of fitna (tribulation) concerning one's religion. Patience with an afflicted husband carries a great reward, and it is permissible to seek a divorce if remaining with him causes harm.