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Hmmm, pls don't strap her into anything. You can harness her. When you are both ready, you hitch or hook to the cart/carriage/wagon. Hmm, will have to check, but I believe you "hook" to farm equipment and "drags".
You can start ground driving before you even get your harness. You want her to be comfortable w/ you behind her asking her to move forward. You don't need a harness for that. You can use two leadlines hooked to each side of her halter to direct her. You don't want her to turn and face you. This one may be best in your situation w/ the halter - since you've mentioned problems w/ hands and fingers (no bit, no blinders to start).
You can introduce her to any terms that apply to driving that you aren't using yet. I figure you are already using "Whoa"? Then train for "Stand", "walk", "walk-on", "trot", "trot-on" and so on. Also some term that means take one step forward - I use "step-up". And you also want a reverse = such as "back" or "back-up". She needs to be comfortable w/you walking on either side of her as well as behind.
Books I recommend -
Breaking and training the driving horse - by Doris Ganton - an oldie but goodie w/ concise and clear instructions, drawings and blk/wh photos.
There are a multitude of books here - Ozark Mini Tack - Books -
Driving
The other one I recommend is the 2nd one down. It is newer and she uses mini horses to show the pics - both color and blk/wh. Star Lake Tack -
Driving Books
There are many/many driving books out there. I've gotten a lot of them over the years - and the most expensive ones are usually the ones I've ben most disappointed with - nice pics but sparse or not understandable explanations that may not be in order that I'm familiar with (and could be disastrous for a newby driver!). Since you/your horses get bored quickly (you've stated that in other posts) - I would highly recommend the book by Cherry Hill called
101 Ground Trainin Exercises
I would start there. Neither one actually gives a time frame to go to next steps - which i found frustrating when I was trying to calculate how long it would take to get a horse started and driving. I've learned there's a reason for that. I know how to ground drive. I didn't know how to harness. I didn't know, when I got my carts, how to hitch. Each horse and driver are different as to learning. Bell and Bit - full sisters - have very different personalities and responses to everything. Bit was pretty difficult to get going - took MUCH LONGER than Bell... There for - you do each step until comfortable and "solid" (I think you will know when??) and then go to the next one that is recommended. You might spend just minutes on one sections and HOURS on another. You can incorporate ground driving while leading and going for "walkies" down the road!
Your horses have had lots of handling and exposure to "stuff" (at least at home) from what you've described. They don't appear to be spooky (most important when driving). That helps a lot.
Harness - there are at least 4 places advertised on this forum that have harness for minis. I've posted links to 2 above. there are many others. I get my harness, now, from an Amish harness shop out of OH. There are other Amish shops closer to you on the west coast OR you can deal with them via phone/mail (most amish don't have websites). You can get very workable and affordable harness.
I don't like using my work harness w/ collars/hames w/ the ez entry carts - the saddles aren't padded correctly for the weight of the cart/shafts & the single trees aren't in right areas for "draft". I do use pleasure driving harness for the EZ entry and show cart.
I don't use a hyperbike and right now not sure I could easily get into one (plus most of our ponies are over the height limits even for the larger size). BUT I do use a sulky cart extensively - I have had repairs done to it and also had a single tree installed. I have driven trails including over branches, downed limbs and big trees (have to dismount the cart, drive horse over, horse HAS TO STOP, lift cart over, remount the cart and drive on!)... I now have the no air tires on it. Not as forgiving for shock absorbtion, but NO FLATS out on those trails. I've driven for up to 4 hours in this cart - my achey hips & back are ok w/ that! Actually nicer sometimes than the other carts/wagons we have. I'm over 250 pounds myself and this cart can support my weight and the ponies - even the 35" one - can pull me in it for hours at a time. One ez entry cart we have is very heavy, the other I had was much lighter. I have other places for EZ entry and other carts I can tell you about, too.
AngC - I have LOADS of pics of us training our ponies to drive... They aren't all perfect, possibly not all safe (we've made our share of mistakes - most I can/would point out). Over the years since 2010, I've posted LOTS OF THEM HERE on this forum. I can post them again.
Bell
Bit
Bell Bit pair
to start... Go to the end of Bell's & Pair album and start from there working your way back to current pics. Bit's - pics of her dead colt at the very end - might not want to go that far. Bit's album does show some of her intro to harness (except the bucking at breeching - couldn't hold pony by myself and take pics at same time). there are a lot more pics than these...