A woman’s labor is progressing. The water sac releases amniotic fluid. The midwife/doctor examines the woman’s cervix. Suddenly, the plan changes from the “routine miracle” of a second birth to an emergency cesarean. Why? The midwife/doctor finds an elbow coming first. Here’s the mother’s story with slight edits, including those to conceal her identity: 

My 2nd [baby was] 9 lbs 11oz…emergency c-section.  I had contractions all day and went into the hospital  where my water broke (I had extra water) and baby turned, ended up transverse and they said I was 6 [cm dilated] and wheeled me away…not really a part of my birthing plan and since it was my first surgery…I was scared; My midwife did say once they opened me up with my 2nd they saw baby head down but arm over head. All went well overall though the recovery was MUCH MORE difficult than my previous vaginal [birth].  My question is…once my water breaks…is there much I can do (as long as everything looks good) to keep this [3rd] baby in position? 

Yes, baby’s position can change in labor and even after the water breaks. Fetal position is most commonly determined at 34 weeks and we know that maternal exercises, positioning and sometimes body work can be used to improve fetal position when necessary.  Even after  the water breaks.

Baby’s position responds to the shape of the uterus and variations in the shape of the uterus that might alter a baby’s position is most often determined by tense and loose ligaments and muscles supporting the uterus and pelvis. Read that twice. The soft tissues determine baby’s position and the bony pelvis determines whether the position matters to how the baby is born. 

Having an arm present first is a clue that baby is lying sideways in the womb. But a clue is a clue and not always the reality.

Transverse lie seems to be a situation where several forward leaning inversions in  36 hours help. But I don’t think she had a transverse lie from this description. It was a reasonable assumption.  If I’m wrong, please forgive me. An ultrasound would have been necessary and yet I have seen ultrasounds mis-interpreted in labor after the water had broken thinking a head down baby was coming and a breech came instead an hour later. 
On my website under Baby Positions about transverse on the drop down links. And the instructions on Forward-leaning Inversion (Inversion)  are detailed to tell how to do it and how not to and when not to. Inversions can be appropriate even after the water breaks in some situations, and I would include this one whether baby was transverse lie or had a compound presentation.
I have questions about how she knew the diagnosis of transverse was correct, or did they feel the elbow and assume baby had moved sideways? That is what I assume from the finding after the cesarean.
A compound presentation means a limb is coming along side the head. In the women giving the description above, baby’s arm was up by the head and bent so that the elbow was coming first.
A technique to help compound presentation is putting the mother into Knee Chest with the rebozo over the entire bum “shaking the apple tree,” as Ina May calls it, would help soften the pelvic floor muscles and buttocks muscles to make room for the baby to descend with contraction surges. 
This second solution for compound presentation and not for a transverse lie. 
A long time will be needed for pushing. Directed pushing is often necessary, meaning a woman is coached to push hard and long. She might pull on a towel or sheet as she pushes. 
The mother above, in my opinion, has an excellent chance of vaginal birth after a previous cesarean (VBAC). My suggestions would include to walk briskly, balance the body with the various balance activities, including Forward-leaning Inversion, and go forward expecting the best. 
If I were her midwife, I would expect a happy, vaginal birth considering the story details shared with me here. I hope she can overcome the curse of the emotional toll of having had an emergency cesarean and be free to be present with her pregnancy today. Present and joyful, she can enjoy her birthing, expecting a lovely VBAC!
Come visit the blog. Spinning Babies Blog. www.spbmembership.wpengine.com