How can a woman who suffers from obsessive-compulsive disorder (waswas) regarding purity and cleanliness fulfill her religious duty towards her husband and stop her obsessions about things becoming impure?

You must obey your husband if he requests intercourse, and it is not permissible to refuse. The matter is simpler than you imagine; you are not required to purify the bed except for what you are certain has been contaminated by impurity, such as madhiy (pre-seminal fluid), and you intend to pray on it. If you do not intend to pray on it, or if you doubt that it has been contaminated by madhiy, then its purification is not necessary. As for other discharges, such as vaginal moisture and maniy (seminal fluid), they are pure according to the preponderant opinion, so their purification is not necessary. Ease your mind and do not pay attention to waswas (whisperings/obsessive thoughts).