Wow, for a minute I thought your dad might be my brother. I'm one of 9 kids, we're scattered across the country, and we have bi-annual reunions. :-) But we kids rotate planning duties, and you're a niece/nephew, so I guess we're not related.
My parents kick in $10K for the location rental, which covers 1 bedroom per kid/family in a large house, and the rest of the costs are ours. Some of us don't fit in one room (too many kids, or kids get older/marry/have kids of their own), so we pay the costs of our families needing more space. It's just pro-rated by space used for the whole week, no matter how long you stay.
With food, every family takes a night to cook dinner for the whole crowd, and pays for the groceries. Breakfast and lunch are on your own, but families often combine on an ad hoc basis. And there's a lot of "who needs my extra eggs" and of course leftover day/night on the final day, as we scramble to use everything up.
That's how we do it. Some comments on your formula below:
1. It's a lot of work to plan all the food for all the varied preferences and ages and allergies and habits of 50 people for 24 meals. So there's going to be a big burden on one person to plan for/buy it all. And there could be eaters that feel like they're paying for everyone else's indulgences and not getting their preferred indulgences. In our experience, everyone buys their own stuff and then pretty freely shares it, and it all works out.
2. Will the lodging formula be applied in advance or afterwards? In advance lets people plan and budget, but what if someone changes their mind and stays longer/leaves earlier? Think through how you'll handle this. If you're going to adjust afterwards, then you'll be hitting someone unexpectedly with an extra charge because someone left early. But if you don't adjust, then someone might resent the person who paid for 3 days but then stayed for 4.
So while I think there's nothing wrong or unfair about your formula, I worry that the logistics of managing it have the potential to cause grief. Especially if, as it sounds, there are some not-so-well-off family members.
Will fewer people staying onsite lower the facility cost? Or is it fixed no matter what?