What is the ruling on enduring life with a sterile husband who demands to take his wife's entire salary, and will the wife be rewarded for this, or is she harming herself and depriving herself of motherhood?

There is no harm for a woman in remaining with an infertile husband. It is sunnah for her to help him search for ways to conceive, the most important of which is supplication, for Allah is capable of all things. He blessed Zakariyya and Ibrahim (peace be upon them) with offspring despite their old age and infertility. If the wife seeks reward [from Allah], she will attain the reward of patience and have her ranks elevated.

However, if she desires children and fears her patience will run out, it may be better to seek separation. Perhaps Allah will provide for her and for him both by marrying someone else from whom they can have children, for Allah enriches each from His bounty.

As for the husband taking his wife's salary, he is not entitled to do so except with her consent and good will, unless he stipulated that she give him a portion of it in exchange for allowing her to work.