My advice would be suss the movement out in the warm up first. You can use the warm up to learn new exercises or prepare for new exercises, and it saves any embarrassment from either you or your g/f if try and train the squat and it looks horrible.
Teach the squat with b/w down to a step. Having a step there helps because it gives her something to sit "back" to.
It sounds like she just doesn't know how to squat with the hips, which is very common. I normally find women much easier to deal with in this case because they normally have plenty of flexibility where as some men are tight as a drum so you have that to contend with as well.
Back to the hips - I start off with an explanation, saying currently you squat with the knees and ankles and we need to learn how to squat with the hips. I then explain what "hips back" means. Then I explain what "knees out" means. I'll show them hip backs back and i'll show them knees out. Then I just tell them to push the hips back and the knees out, these 2 thing are all I want them to think about. I tell them depth is irrelevant, we just need to get the movement right and the ROM will come.
Most commonly with people who lack body awareness, they may get one and not the other. So, they may push the knees out but they initiate the movement by shooting the knees forward. Or, they may initiate with the hips but the knees cave in. In that case you tell them they're half way there, "you're getting the hips back, now you just need to push the knees out, too", or, "you're pushing the knees out perfectly but you need to start by reaching back with the hips".
Sometimes, like magic, it just clicks and it's as if they've been squatting like that their whole life (your brain is hard-wired to squat like that). Other times it will require a lot of thought just to do it with bodyweight, in which case I ask them to practice it daily and I won't load it in the workout until it "clicks".
Pushing the hips back and knees out will fire up the glutes and hammies, which is what allows you to squat back - I would argue that a toddler squats back, btw, and not down. Semantics, really, but when you think of squatting as sitting back rather than down it tends to help.
This is the initial approach I use. The clients reaction depends on where I go from there. There's a variety of cues and tips for squatting. For example, holding a light weight or med ball out in front for a counter balance. Wrapping a light band around the knees to "emphasise the mistake" - this, btw, can completely transform a squat in seconds, as the band forcing the knees in causes an automatic "knees out" response.
I stay away from a heel lift because I want people to get back on their heels. Normally if you fix the hips this will happen as a side effect. I know some people use a heel lift initially and progress to flat but it's not something I do. I quite often ask people to remove their shoes because they already have a heel lift on them.
Anyway, nail it with body weight, then go to goblet squats and use it as an exercise. When it's just like "riding a bike", then all you need to do is teach the front squat bar position because she will already be able to do everything else without much thought.
that was solid gold Kenny, exactly what I was looking for, thanks.