HUG
You are certainly NOT a bad mommy!! Far from it. I can feel all your determination and committment.
You know he could be fighting you because you have too much milk or an 'overactive letdown' rather than too little. Or it could be because he is finding it hard to switch between the different flow of bottle and breast - what Tracy calls 'flow confusion'. Are you using a bottle with a slow teat? - Tracy talks about using a variflow bottle or haberman feeder to help with this problem.
There could be lots of things going on. You could wind him earlier on in the feed and break him off to do it as spitting up can be seriously affected by wind.
First off, you really need to speak to your doctor about the possible reflux and find out whether you can get some proper medication if that's what he needs.
Secondly, I would suggest you call a breastfeeding helpline - there are numbers on the FAQ page. Talk through your situation and you could get some great tips.
Have you found the reflux board too:
https://babywhispererforums.com/index.php?board=13.0Good Luck.