The economy is getting tight, groceries and gas cost more. You all may have planned this trip months ago, but face it, life happens. Maybe months ago she had the money, but perhaps something you're not aware of has come up.
Perhaps she always feels pressure trying to "keep up" financially, but has finally reached a point where she can't keep up. All I can say is things must be tough for her, because in the current culture we live in today, there is nothing more humbling than having to tell others you don't have enough money to do something. She's got guts. Furthermore, she has great faith and trust in you as a friend. She's trusting you'll be understanding, and will be fair to her and her child. She clearly wants to be with the group and have fun. I don't think she wants a handout, and I don't think she wants to be a wet blanket. But obviously she's facing some challenges of her own and is hoping you'll cut her a break.
The reasons could be endless why she's asking for concessions now. Does it really matter what those reasons are? I guess I'm wondering why you're so determined to do these costly activities, even if she can't? It sounds like the trip was orginally planned so that your entire group of friends and their kids could spend a fun time together.
I may be reading this wrong, but from your tone, I definitely pick up dismay and maybe even a sense of entitlement to call the shots on the entire trip just because you're providing the tent, and other accommodations. I don't know you or your friends nor the dynamics of the realitionship. I guess I'd recommend taking her feelings into account, and perhaps you consider whether it's fair to go ahead and do activities that would exclude this one friend. I think her feelings would be hurt for sure if you did. It would probably put a rift in the friendship amongst all of you..and would probably ruin the entire trip mood-wise. Is it worth it? Perhaps a refocus on why you're all getting together in the first place is order. Whatever you do, don't get caught up in semantics, or into a tit for tat about whether activities/things are divided amongst yourselves equally in a monetary sense. This is a quick way to put a real damper on the whole weekend for everyone, and as I already said, probably will dampen the friendship in the long haul as well.
In short, I ask you to consider this; Is this a valued and well loved friend? I think true friendship isn't measured by how much you can get out of a person...or whether or not they're chipping in as much as you. That's like little kids fighting over who gets to use the slide next. Real friendship is measured by the amount of love and support you and others give each other.
If this friend has sat up through the night commiserating with you, has had you to her home for dinner, watched your child for you, or shown any other measure of friendship or love toward you and your family, she and her child deserve your compassion and consideration. Don't harden your heart to maybes, even if she had something as serious as a gambling problem or worse, you owe it to her to listen to her plea and be compassionate of her plight. S
Most likely, her financial woes aren't because of something so dire as addiction, but rather she probably doesn't want to grovel for a handout so she and her child can tag along, and is asking in the best way she can to help her out. If so, be a true friend and get her help. If it's just an honest shortage of money, be a good friend and give her a break.
Save the "extras" for when it's just you and your child, and go back to the drawing board with the entire group and find affordable activities the entire group would enjoy doing. Afterall, maybe the others invovled are feeling the same thing but aren't saying so.
Last but not least, most camping sites have plenty to do that don't cost money. There's always scavenger hunts, hiking and biking. What about fishing or onsite swimming? If there's a nearby town, window shopping at the local shops is cheap and fun. Get creative. Get a boys scouts / girl scouts official camping guide/book for camping activities that are both creative and affordable.
Just some food for thought. Good luck in what you decide to do.