Please talk to your Service Unit leadership. They should be experienced leaders who can give you guidance and advice. If you're not active in your GS Service Unit or don't know what I'm talking about -- contact your GS Council and get your Service Unit information, especially contact information. Some SUs are stronger than others but it's a good resource for new leaders to get input from more experienced ones in your area. I am not saying tell your SU and they will handle it for you because that's not how things work; I'm saying, ask them for advice as fellow leaders, especially those with experience at Daisy level.
I disagree entirely with the person who posted that co-leadership is a bad model; it works wonderfully in our troop and in some others I know, but the key is to have two co-leaders who truly are on the same page and who communicate extremely well with each other. It sounds like you and your co-leader do not communicate and she does things without consulting you -- note that I am saying "consulting" and not "asking" because if you truly are a team it's not a matter of permission, it's a matter of consultation, together.
Have you had a parents' meeting for this year? You need to. I would hold a parents' meeting where you and the co-leader and parents discuss the year's plans, what you expect to happen, rules, etc. That's usually done at the very start of the year and you might have had one already....That is a perfect time for parents to express -- in a civil, GS way -- "Our girls love patches, but we want them to understand what the patches mean. Is there a way to tie patches to the program that they are doing at meetings?" Frankly, if you are close to a parent who feels this way, you can plant the seed by asking that parent to bring it up at the meeting. I agree with the parents that the girls should not be handed patch after meaningless patch. You need to be already moving on to the girls earning the Daisy petals -- that is your structure for the rest of the year and requires specific activities so get onto that now; the paperwork and bank stuff can be done as it comes up but it's past time to move on with activities. That will get the girls to understand better that they EARN petals.
I am not going to be quite as tough on your co-leader as some other folks here. Sounds like she is unfortunately carried away with ordering cute patches. I'd tell her that your troop has spent X dollars on patches that aren't related to the Daisy petal program and now it's time for the girls to start earning petals. If she tries to say "Oh, I'll buy patches on my own," you might want to tell her that that's not fair to her -- and that the girls will get more out of earning petals than having patches. I would not make this the make-or-break, split-the-troop issue -- I would be more forceful with her in terms of, "At the next meeting the girls need to start earning their first petal. Let's discuss what the activities will be and how many weeks they will take, " etc. Move ahead and frame everything in terms of girl activities -- not paperwork on your end and patches on hers. These girls need to be doing more, or they'll get tired of patches soon.
I'm sorry you and she arent' having a good experience as leaders and hope you can get through this year and form another troop over next summer that is much more oriented toward real activity, not just go, go, go, as you put it.