Most activities a doula performs do not violate any laws of Shabbat. Reassurance and physical contact, which do not involve chilul Shabbat, would certainly be permitted. In a situation where a woman is depending on a doula, and would be distraught without her administrations, the doula would have the same status as a husband, who is permitted to assist his wife for the purpose of yishuv hada’at (emotional well-being).

Regarding getting to the hospital and taking a phone call from the client, it is best for the doula to seek counsel from her own rabbi with these issues. Since personal factors would be taken into account in this type of ruling, it is best to consult with a rabbi who also understands the needs of the particular client.