Husbands, Mothers-in-Law, and Going into Labor on Shabbos

When a woman is in labor and has to go to the hospital on Shabbos, who may accompany her?

Doing melacha for a woman in labor or a חולה שיש בו סכנה is permissible to calm their nerves.

Rav Moshe discusses why a husband is permitted to accompany his wife in the taxi on Shabbos.

What if the wife doesn't ask the husband to come, can he still go? What if she doesn't want him to come, can he still go?

What if she wants her mother to come as well?