I'm coming into this late, but as an experienced girl scout and cub scout leader, and trainer, I wanted to add in a couple of thoughts for you for this coming year.
First of all, I think it's a very good idea for you to split with this co-leader. Clearly, the two of you are not a good match for whatever reason. As you get your Brownie troop started, however, please keep the following things in mind, as they are important aspects of the GSA model.
1. Troops should be girl-centered and girl-run, according to age and stage. The adult leader is there to facilitate growing independence and leadership skills in the girls. She's not there to be an autocratic decision maker. If your co-leader wants to push you around, you can bet that she will NOT understand the principle of growing a girl-run troop. As a Brownie leader, your first task will be to help the girls decide how to run the troop, what kinds of projects they want to do, and what the behavior rules and repercussions should be. We started out every year with a round robin discussion of these topics. We created a "speaking stone", which got passed around the circle. You could only talk if you held the stone, and everyone got to submit ideas to be voted on. All were encourage to talk. No one was allowed to use the words "dumb", "stupid", or anything similar. All ideas were written up on a flip chart, and than distilled down to a half-dozen simple agreed-upon rules that were written on a piece of foam core and posted at every meeting. Troop positions were decided upon, and then assigned randomly (pulled from the job jar). After the first assignment, jobs rotated in a set pattern every two weeks so that everyone had an opportunity to perform in each leadership role at least twice a year.
2. Keep in mind that Try-It's are fun to earn, but they are not the be all and end all of scouting, and they are not a competition. A good troop will include a balanced mix of working together to earn Try-It's, doing age-appropriate community service projects, and just having fun. Participating in all-council events should be encouraged, from celebrating Juliette Gordon Lowe's birthday to wide events run by local Cadette and Senior troops. Also, GSA has a wide range of additional programs in topics such as reading, business skills, leadership, first aid, being a good citizen/friend, etc. Patches and charms are as much fun to earn as Try-its! Participating in a local 4th of July parade was always a highlight for our girls. (We lived in a small town).
3. Get outdoor leader training and first aid training, and help your girls learn to enjoy camping. The first events should be small and easily contained, with a lot of parent help *as directed by the girls* (that is, you help the girls decide what needs to be done, and they direct the parents to help out). A good way to start is an overnight, inside sleepover, advancing later to "camping out" in someone's backyard. By your second year of Brownies, consider a camp out at a campground close by. And yes, a girl or two may get homesick and need to leave in the middle of the night.
4. Dues are very, very important, and they should be paid by the GIRLS, not the parents. It's a good idea to charge a small fee at registration to have start up money, but after that, the girls should decide what reasonable dues are ($0.25/meeting is good for Brownies), and they should be encouraged to help out with chores around their homes to EARN the money, not just ask their parents for it. Have a parent meeting at the beginning of the year to get the parents in line with this (and other ways the troop will be run). The treasurer will be responsible for collecting the money and checking off the names of girls who forgot, so that they can bring it the next time. After 3 "forgets", the leader will need to talk to the girl and parent in private to find out if there is some financial problem with paying dues. If not, the girl should be told to sit out for a short period from some fun activity until she learns that it is her responsibility to be a good citizen of the troop, and bring her dues (a good introduction to paying taxes!). Make sure you keep careful books, though, and a separate bank account for troop money.
5. When I was leading, Daisy's were not allowed to sell cookies. I think that they can now, but with restrictions. Cookie selling is a hard job if you want to raise a lot of money for your troop. Even if the girls want to sell, parents often hate to have to support the effort. I can tell you that my daughter and I put in a ton of hours because she wanted to be the top seller in the troop and the region (in her best year, she sold over 2500 boxes of cookies, about half of which was in presales. Selling was not nearly as difficult as delivery!). It took a ton of time out of my day, but she absolutely loved the activity and was good at it. (She'll be heading to college a year from now and has decided on studying international business, based partly on how much she loved selling cookies, developing marketing ideas, and advertisement.) One thing you should know about cookie sales -- it is a HUGE headache from the perspective of the cookie mom. There is a ton of bookkeeping involved and it's always a job and a half making sure that you're keeping enough stock, have easy access to replenish it, and that the girls are accurately accounting for boxes received, sold, and remitted. It also can become very competitive and a sore point in troops when one or two girls out-sell everyone else, and especially if the troop decides to use the money in a way that the top sellers aren't happy with. (Use of money earned for the troop should always be a troop decision. GSA is both democratic and socialist!) In my opinion, the best way to ensure reasonable equity in the process is to make some amount of booth sales mandatory for all girls. Also, if your local council runs a Cookie Kick-off activity, make sure to go. It's usually a very fun way for girls to learn about the products, the safety rules for selling, how to sell, and to get excited about the process.
6. Get more leader training! Yes, I know it's a pain and there are hours and hours of it. But, it is really important that you learn to run each age and stage of scouting. If your council has monthly round-table meetings or other leader get-togethers, go. The more training you get and the more you talk to other leaders who are successfully implementing the program, the easier and more fun it will be for you, and the more rewarding it will be for the girls.
7. You should have as much fun being a leader as the girls are having in the program! Enjoy yourself and the opportunity to be creative, but always remember to stay flexible and compromise.
My co-leader and I ran a very successful troop for years. I also ran my son's cub scout den and pack, until he advanced to Boy Scouts (He's Eagle, now). The saddest day of my life was when I had to quit because we were moving and I had to return to work full time. I hope that someday I will be in the position and have the time to be a leader again. You don't have to have a daughter in the troop to be the leader. I think sometimes, that it's better that way. In fact, one woman I know is still leading and camping, and she's in her eighties!