Wow, that's just full of red flags. I don't think you can just leave it to Jesus, or even a higher power if you prefer, to properly handle the situation. I'm assuming that you are unable or unwilling to cancel/defer this trip.
1. Can you stay in a motel/hotel while you are there and only engage with them during the day when drinking may be less or not present? You can explain this anyway you want, including that you are not drinking and that it makes you uncomfortable to be around them when they do consume. It seems to me that removing yourself from situations of alcohol use is paramount and worth the expense if you can afford it.
2. What about cutting the length of your stay to achieve the essential things? The shortest time you have to deal with it the better, especially around your brother, the better. You can say you have other pressing obligations that require you to be home.
3. If you can, set up arrangements for seeing that bills are paid electronically by you or that you can monitor that this is being done properly.
4. What outside services are your parents receiving, such as elder care visits, meals on wheels, etc.? If they have dementia symptoms, I wouldn't trust it to your brother to provide them appropriate oversight and help. Have their medical appointments been attended to and/or transportation services for regular care been defined? Does somebody check on them periodically?
Remember the priority of your recovery.