Hi & welcome to HF!
but nowhere near big enough to hurt the new horse.
First & foremost, I'd want to make sure of that. Moose may be built like a... moose, but that doesn't mean she is necessarily fit for carrying a 'heavier' rider. She may be very unfit &/or have body or hoof issues that hurt her 'under load', the bit may be hurting her or her teeth are bad, making her 'antsy'. She may have a saddle that hurts her... etc. Of course, it may be purely 'behavioural', that she's only ever been ridden by a featherweight, but rule out physical possibilities first. And if you still think it's 'just' lack of training, then as you're 'newer' to horses, find an experienced trainer/rider to teach her it's OK.
Moose tends to throw her head up and down, will not stand still, and tries to go her own direction. She even does it with me who weighs a little over 90 lbs,
Which sounds to me that it *might* be HOW your mother - and you to a lesser extent - is riding. Perhaps you're riding with too short/tight reins, not giving relief, not rewarding her for doing the Right Thing... And of course, 'tries to go her own direction' - of course it's worth a try. Almost all horses will test you out, see what they can/can't do with their new rider.
She rides in a simple dee ring single jointed snaffle or a halter, with a tie down.
Ditch the tie down - it's possible, depending how it's set, how you're riding... her previous associations with it - that tying her head down is the main problem. It is very likely at least contributing to it.
So... after ruling out physical discomfort/pain, after having an experienced rider/trainer establish that she is OK ridden by a heavier rider, then I'd suggest you find yourselves an instructor, or at least an experienced rider, willing to help you learn to ride as well as possible, to ensure you're not the cause. (Meant respectfully - none of us know everything & we all have to start somewhere)
(PS I only got like 4 hours of sleep so this is probably riddled with spelling errors, apologies lol)
Didn't notice a single one - you're doing better than I do on little sleep!