Should my mother form an LLC with our family cottage?

There are ways to do this with a Trust, and there are ways to do this with an LLC. There is no one 'best' way to do this. In either event, your plans should consider what to do with the kids who don't want to partake in the group.

The logistics of this sort of property sharing is complicated to say the least, and unless all the pros and cons are weighed you will likely hurt someone. For example, your mother may decide 'this is the deal, if you don't want to work with your siblings, then you get nothing'. There is nothing wrong with that however, unless all the sibs can easily afford the maintenance, taxes insurance etc there will be bitter feelings about this. There are usually ways to structure 'buy-outs' for heirs who don't want to participate so everyone is treated fairly, but this requires lots of thought.

The other issue is that placing the property into an LLC can uncap the property for tax purposes if it is not done correctly, so you have to structure things properly if you want to avoid that