I think you split between the number of people going. So you each pay a third.
I had a very similar scenario this summer, except we went away for a week with 2 other families. We all have different number of children (3, 2 & 1).
I suggested we split rental costs by person, the other family wanted to split by bedroom, which meant that the family of 5 paid the same as the family of 3.
the family of 5 would use much more water, utilities. - 5 showers instead of 3, 5 people flushing the loo instead of 3 etc. We came to a compromise eventually somewhere in the middle and had a lovely time.
I also received the same answers as you suggesting you look at the cost difference between going away by yourself and inviting your DB. I don't think that's the point at all. You want to go away together so you pay the cost of the chosen accommodation.
Think of it as total cost, not just by bedroom. You're all using the same amount of space, gas, electricity, furniture etc.