If she drops her head when you "wiggle" the reins then you need to start tightening your abs, bringing your elbows back to your hips and bearing down slightly with your seat bones while gently squeezing with your calves. This will do a whole bunch of things at once, it will engage her rear end to carry herself, it will lift her back into your seat so that she can round and it will make you strong enough to hold her gently in frame as she goes along. Practice taking a deep breath in, squeezing on your reins and gently holding a little tension on your reins as you exhale and gently squeeze your calves. This will help you learn to half halt on the inhale and engage the hind end on the exhale without throwing away the good connection you got with your half halt. The key to framing a horse into a nice "head set" is to give them enough contact on their mouth to balance them and let them stretch onto the bit but not enough contact that you're forcing them into a head down position. If you lock your wrists and elbows, and bear down with your seat hard you're holding them in frame. If you're holding your elbows and wrists firmly but with a little give and you can feel a little tug in your abs you've got a firm contact and if you're just barely holding onto the face and they're in frame you have a light contact. A horse that is just learning to develop the muscles and strength needed to "go in frame" or "on the bit" needs a little "firmer" contact. This is because they need you to help them hold the frame. They don't however need you to "crank" them down into it or force them to keep it when they get tired.
When you do the inhale exercise only make it last a stride or two them release and pat her. Let her stride out a few strides and then do it again. Start with a few good strides of connection where she's going where you want her. Feel it, memorize it, analyze where you are and what you did to get it. Trial and error...don't be afraid to make a few little mistakes. Experiment with half halts, breathing, and different leg and seat aids as well as hand aids. Once you find what works, just keep doing it and gradually ask her to hold it longer and longer. Generally, once you find the "sweet spot" you're good to go and they pick it up fast and retain the knowledge of what you want them to do. Sorry if that's a bit confusing, feel free to message me if you have questions or need a better/different explanation.
