OK, I have absolutely no experience with the breed, but while some types can be a little... trickier, more sensitive than others, I think it's not a reason to just assume she's unsuitable. That you are inexperienced & have no hands on help, that she is only 6yo & your daughter is (I imagine) a 10yo beginner are indeed reasons to suggest that you'd be better with an old 'been there done that' pony.
Your daughter, at 10yo, if she's been dealing with horses for the last few years & has been taught really well, may indeed be up to training the horse(in which case, ask her for pointers), but I imagine that if you're not experienced, your daughter is also a beginner, and if you don't know what to do, being 10yo doesn't mean your daughter will. And how are you going to teach her, if you don't know yourself? Blind leading blind isn't the best of tactics.
Bit of an aside... you said you separate them for feeding & there is no grass in their small paddock. Just checking that they get hay as well?? Horses aren't built for going hungry & need little & often or free choice access to roughage like grass hay. And maybe not such an aside, what else is she fed? As a fat & feisty pony, she doesn't need any more energy from supplementary feeding. Too many 'beans' might be a part of the problem. Nutritional balance could also come into it, effecting behaviour too.
Another possible aside, it appears your daughter in the pic is small enough to afford a bit of growing before she's too big for the horse, but your 15yo sister, if normal sized, is quite possibly too big for her, so hurting her, exacerbating any saddle issues,(& extra discomfort on those feet) and effecting the horse's general attitude because of that.
If she moves as you set the saddle down, remove it quickly and make her move. When she first moves, it's her idea. Now make it your idea. The direction doesn't matter. The trick is to keep her moving after she wants to quit. Develop the attitude you plan on killing the horse
You will soon learn that there are conflicting opinions galore to sift through too! The above is one that I couldn't disagree with much more. Firstly, horses learn from *instant* associations, so if the pony moves because she doesn't want to be saddled so you remove it, be aware THAT is the consequence for her moving. Doesn't matter what comes after, it's what happens *at the time of* the 'bad' behaviour. Now, when you 'make her move', especially if you want her to be terrified of you, feel you're going to kill her, it will be an unpleasant punishment for her, and I don't want a horse to hate their 'work' - on the contrary, you want the horse to learn to *enjoy* and feel confident playing your games. And thirdly, I don't EVER want to have my horses afraid of me, let alone to the degree of trying to make the horse fear death from you - that is just so many kinds of wrong to me. And fourth, it is back to front, that if you want the horse to stand still, that you would make he move. And fifth, I couldn't think of anything worse than making your horse think you might kill it. Did I say that already??