Is the first wife entitled to demand spending a similar period (two months) with her as compensation for the husband's absence from her due to his secretly spending the night with the second wife, knowing that the first wife was ill during that period?

The husband must be just in dividing his time among his wives regarding overnight stays, such that he spends an equal amount of time with each of them. It is not permissible to allocate the night to one and the day to another, because the division is reckoned by night. If he marries a virgin, he may stay with her for seven nights, and he does not have to make these up for the others. If he marries a non-virgin, he stays with her for three nights, and he does not have to make these up. If he stays with the virgin for more than seven nights, he only has to make up the excess to her co-wives. However, if he stays with the non-virgin for more than three nights, he must make up the entire excess to the other wives, unless the first wife waives her right or part of it.