This is a lifetime dream for me and I'm not giving up now!
I know how you feel too - I've been through several ponies/minis who I didn't feel were suitable for driving or life got in the way, or all I could afford was junk equipment. Then I found the mini I love, Lacey. And coincidentally got a great contract job so I could afford her
I finally bit the bullet and got my mini Lacey trained by Lori Rafter, who did a great job. When I took her home, I got a "quality" new pipe cart that for various reasons wrecked my first couple of months with Lacey (defective tube, missing parts, poor construction, made me sick to look at it). After I got it fixed to the point where it was usable, I sold it. Apparently that kind of quality is acceptable in pipe carts - must be me, haha. I was so mad at the time
But I'm over it now... really
Then I got a nice little roadster type cart for cheap - she liked it and I liked it, but it crippled my back.
Finally I got a nice cart which I like and rides well.
Then my trailer broke - then the truck broke - both fixed now.
Then the harness started causing problems. So I am now waiting for her new Comfy fit harness (which isn't money I wanted to spend, but I realized if I'm doing this, I need to put the right ingredients in. Come on, Universe, I need another good contract job to pay for the harness, haha.)
Then I had to solve her attitude problem caused by the harness and me.
I would say, don't give up yet. Check her harness and see if you can have some lessons with your own horse. With Lacey it was the girth strap and the wrap strap chafing her sides (belly band too short) and probably me sitting too far back in the cart and wrap strap too loose (thanks mini drivers at the Centreville fair!)
If you drove her a few times without your daughter and had a feel for how she is likely to behave, then you will have a better idea of whether to include your daughter at this age.
Good luck and I hope you give it a bit more time.