You know how when you're riding a bicycle and if you stop pedaling, the bike slows down? Unless you're going downhill, the bike no longer carries you along unless you're pedaling. That is what I meant about your horse acting like a bicycle. You should be able to put her in walk, and stop pedaling and she continues on without slowing down. Pedaling on horseback is nudging her to keep going with your legs/seat, whatever. You want to ge the feeling that you put her in walk, and you sit still and she carries you along without you having to keep telling her to go. This should be done at slow walk, forward walk.
A way to train this into them is simple. Grab a whip for reinforcement and ask her to walk and then be still. Don't shove with your seat, dont squeeze her with your legs, don't do anything. If she stops or slows down try tapping her shoulder with the whip instead of her haunches so that you do something different(she already has a learned response to the whip on her haunches, so do something else). The moment she gets her feet moving again, be still. Repeat this until you quietly ask her for walk, and she walks without you having to "pedal" her along. Do this at trot. Try not to nag at her at any time, just repetition and timing will give you the most success.
The old rule of thumb in riding is that if you don't have it at the walk, you won't have it at the trot. So you definitely don't have it at canter, so don't go there, otherwise you will only be practicing what you don't want.
Once you work on this for a few days and she's feeling lighter and more responsive you'll try the canter. Do not be too picky on the lead, just worry about whether or not she's moving forward. Once she canters don't bicycle her along. If she breaks to trot, re-balance and ask for another transition. Don't nag at her to keep the canter. The more times she picks up canter, trots, and then canters again she will start to hold the canter for longer because its easier to keep moving instead of a million canter trot transitions.
The goal in mind here is not about getting her to canter, you can improve the canter later. For now, focus on getting her lighter and more responsive to smaller aids.
In riding, a horse's energy is like a river- guided by the banks but not stopped by them.