Because this is not traditional, you will have people that will be uncomfortable. You don't want their discomfort to be attributed to the bride. I would plan regular games (tons of websites out there for ideas) and just offer to buy some of the gift baskets the bride has (she could use the cash) and use those for prizes.
On the bottom of the invitation, print something like, "If you wish to use the money tree, just bring your gift in a small envelope." Then you could provide a spool of ribbon and a hole punch and a little tree. If you have no tree, just draw one on a piece of poster board. You can attach it to a bulletin board and offer thumb tacks or you can just have them tape it to the tree.
There are always going to be people who give money gifts and gift cards. Some people have a set gift they always give, whether it is homemade or has a special meaning. Don't take that joy away from them. If she gets something she has already, let her decide if it is something she would love to have brand new.
Making this party a fundraiser sends the message (true or not) that this couple is not good at money management and using their wedding to get some money. Instead make this a party to celebrate their marriage and their lives. People want to come to celebrate. I am sad that the bride would go along with this. I'd rather hear that she just wants to celebrate not raise funds...