Prioritise kids taking responsibility for their own belongings, clothes, toiletries, sleeping bags, sleeping mats and any toys they want to take, they carry! OK, if you have really little kids, maybe carry their sleeping bags for them.
My 8 yo DS and I have been to several festivals car free. We carry our gear in packs, I have tried a wheeled case or bag and folding trolley but really is hard going over open fields even if no mud! Don't expect to be able to hire a trolley when you get there, Mr Trolley and others tend to set up in the car parks and no where near coach drop off points.
Take multi purpose items, if you want to take chairs, go for lightweight compact ones or even stools, each person (including children) to carry their own.
We always take camping stoves and some food for breakfast + one meal each day but often will buy some staples there like baked beans and tinned tomatoes, yes, I know they're pricier at a festival but I'd rather not have the extra weight. Take frozen wine or juice to keep your cool bag cool, if you take ice packs, you have to carry them back!
Going to a festival soon-ish and want to get prepared. Camping is not a problem but camping with several thousand other people is not something I've done. We are not taking the car (long story) so we go in with what we can carry. What would you prioritise and what should we totally avoid taking/doing?