Lisa Barrett just posted about resuscitating the newborn. I love the photos at the end showing how to resuscitate and evaluate a newborn without cutting the cord or removing the baby from the mother. She shows pictures of a breech water-born baby receiving positive pressure ventilation via a bag and mask. The baby remains with the mother, who is still sitting in the birth pool.
Here is an illustration of a resuscitation from Anne Frye's Holistic Midwifery Vol. II.
Resuscitating a baby without removing it from its mother is certainly doable, although of course much less convenient for the birth attendants. (One might ask, of course, why convenience so often trumps what is best for the mother and baby.)
The one time I have resuscitated a baby was after a water birth. The midwife was still en route when the baby emerged. The baby was floppy and didn't respond to stimulation. The parents helped support the baby in the water while I positioned the airway and did mouth-to-mouth, which was all the baby needed to come into her body. (I was at the birth mainly in the role of a doula, although I had also begun an apprenticeship with the midwife. This experience spurred me to become certified in NNR. I took the course from Karen Strange, who I highly recommend if she is coming to your area.)
Home birth attendants have devised a nifty & portable contraption that substitutes for a warming table if the baby needs a warm, firm surface for resuscitation (for example, in the rare occasion that chest compressions are warranted). You put a large plastic cutting board or cookie sheet and some receiving blankets on top of an electric heating pad, then wrap everything in a pillowcase. You simply carry the "warming table" to the mother & baby, rather than remove the baby to a warming table. Midwives will often place folded towels on top of their "warming table" during a labor. This warms up the towels and keeps the cutting board warm.