Natural Birth & Parenting

I had a couple contractions an hour all day on Halloween. I was 41+1 so finally having something happen was encouraging. Jay put Trent to bed and ran to the store for a few things and I went to bed after a bath about 10pm.
Trent woke up at 1am and despite Jay trying he
never went back to bed. About 1:30 I had a really intense contraction
that was hard to handle laying down, the next contraction my water
broke. I changed and spent a while handling them on hands and knees and
then got in the tub. When the tub wasn't working I had Jay call my doula
because I didn't want to deal with contractions by myself anymore (he
was entertaining Trent). My doula (M) showed up about 3am and
contractions slowed down. I thought for sure that things were petering
out and I'd be sending her home. She did counter pressure on my hips
while I stood during contractions-standing made them less intense. She
suggested I try to rest in between so I sat on the birth ball and put my
head on the bed.
At this point the contractions got stronger and every time I had one I leaked more amniotic fluid. They were so intense I felt like I couldn't handle them and wasn't getting much break. I thought to myself if I wasn't getting close to transition I wouldn't be able to do much more and even though I knew an epidural wasn't going to remove the contractions the allure of one was definitely there. M suggested I pee since it had been a while and I got very little out and had back to back contractions while I was sitting there. Once I stood up I decided to get in the pool because that was going to be my last thing I tried before I gave up. I got in on hands and knees and the next contraction I let out a guttural noise and my body started pushing. M asked what I was feeling (she was still doing counter pressure) and I yelled "I'm pushing". She said "yeah I realize that" and I heard her get her phone and say "come, she's feeling pushy". My midwife (K) lives across town and I have no idea how she managed to make it from being asleep in bed to in my birth pool in 30 minutes but she did. Once I started pushing I finally realized that baby was going to be born at home and the pain of contractions was gone and replaced by the pain of a baby crowning. K showed up and the next contraction her head was out. Next contraction I pushed but she was still in so K reached down and upwrapped the cord from around her. Next contraction I pushed and she still didn't come so K felt and noticed that she had one shoulder still inside but it was already past my pelvis. So she told me to push as hard as I could on the next one and finally she was out. Later we realized that her chest was larger than her head so that's why she was a little hung up. Jay got in the pool at the end and caught. M took a video while we peaked and saw that she was a girl.