Is it permissible for a Muslim woman to uncover her shins and thighs in front of another Muslim woman to remove hair, if she is ill and unable to remove it herself, and this is to please her husband?

A woman is not permitted to refuse her husband's bed merely because of the presence of excess hair, as you mentioned, unless he desires that. What might prevent or harm the husband should be removed. The 'awrah of a woman in front of another Muslim woman is what is between the navel and the knee, and it is not permissible to expose it except out of necessity, such as for medical treatment. It is not permissible to expose it merely for the purpose of shaving pubic or thigh hair. It is forbidden to let another person shave the pubic hair, except for the wife or a female slave, though even then it is disliked.

If a woman is unable to remove the hair herself, and the pubic hair becomes long or the thigh hair causes her discomfort, then there is no harm in seeking the assistance of another Muslim woman, but this is a necessity to be judged by its extent. It is not permissible for a woman to look at what is between the navel and the knee of another woman except out of necessity, such as a midwife during childbirth, or to ascertain virginity, or to treat a wound or ulcer in a place that men are not allowed to look at.