I have had 2 c-sections... the first because I had complications and it was an emergency, and the 2nd was planned. Both my babies were born at over 8 pounds each, developed perfectly and healthy.
C-sections, in my case per my Doctor, are routinely 'planned' about 2 weeks before the projected due date...so that to avoid the "going into labor" which can complicate things if there is a concern... if a woman goes into labor early, unexpectedly, and has a "risky" pregnancy...the woman can possibly hemorrhage and this bleeding and rupturing can put the Mother AND baby at risk/death.
So take heart... a Doctor knows what they are doing.
A baby being born at 37 weeks is fine... and in the "safe" zone. The baby is sufficiently "developed" at this point... and it should be fine. They will take proper care of the baby after birth... and make sure all is well with baby and Mom.
The Doctor can address any concerns of the Mom.
Just provide any support if she asks.... pray for her, and all will be well. I'm sure she and her husband must be wondering about it too. If the doctor is prescribing bed-rest... then she would and should do that.
Main thing also, is to try and make sure she is not feeling "bad" or disappointed about having a c-section versus a vaginal birth. For some Moms, this can affect them. A birth is a birth... vaginally or via c-section. We all bring life and our babies into this world, and it is a special time for a woman. No matter what method.
After her c-section... let her and Hubby enjoy and recover as they need to. For you as Grandma... just be sure you let your dear daughter know, that you can help in any way SHE needs to, and to just ask you. There is a recovery time after a c-section... typically 2 weeks of "rest"... although each woman recovers differently. Research c-sections, and this can give you knowledge on what to expect afterward. My Hubby for example, stayed home with me for the first week, and then the 2nd week my Mom stayed home with me to help. They both took turns to help drive me around to my follow-up Doctor appointments and baby check-ups (since after a c-section a woman can't drive). No matter what or how your daughter and Hubby want to handle it... let them adjust in their own way, since it is their 1st child. You sound like a dear Mom... and don't worry, your girl will be fine. This is what I & my Hubby did after my c-sections. It worked out well. The recovery time was fine.
All the best, and take care,
Susan