I remember the "ring of fire" burning pretty bad, BUT... I was no longer feeling contractions! I was in a hospital (preterm) and was doing directed pushing (which you DON'T want to do). The first push, I was a little scared to push. I did these itty bitty brief pushes, and then the nurse said "No, just do one long push", so I did, and it was very effective and once I actually got the nerve to give that push, it felt alot better.
The second push, I wasn't feeling an urge to push at that moment - this is where directed pushing sucks and caused me to tear with a <4 lb baby.
My body was not given time to stretch appropriately. But on that push, his head came out. The 3rd push was not a big deal - the body came out pretty quickly and easily once the head was out.
Honestly, while that ring of fire was probably the most painful part of labor for me, it also was one of the easier ones to get through, because my baby was RIGHT THERE and I was about to meet him!!!
I think the hardest part to get through was transition contractions, but thankfully, I remembered that when I felt like I couldn't do it anymore, it was almost over, and sure enough...
During pushing, I never felt like I couldn't do it... and that says alot.
Since you're having a homebirth, I know you will do GREAT. Pushing is the best part of the birth! And if you're listening to your body, I think you'll have a good experience. YOU CAN DO IT.