For sequencing purposes, you'd need to code the condition or complication that created or caused the plan for a cesarean.
If you check under O75.82, there is an instruction "Code first
to specify reason for planned cesarean section such as: cephalopelvic disproportion (normally formed fetus) (O33.9) previous cesarean delivery (O34.21)" which would prompt the use of O34.21 as "possible delivery problems".
Then, of course, you'd have to use the Z code to indicate the outcome.
So you'd get O34.21, O75.82, Z37.0
This is a good reference (see pg 61): http://icd-10online.com/wp-content/uploads/2014/05/2014-OB-new-ppt_layout_illust_final-051914.pdf
Regarding the admit, just to clarify, the patient came in due to spontaneous onset of labor, correct? I only ask because if she was not in labor and was admitted with the plan to do the C-section, that'd change your coding.