Hmm…I really like the other person’s answer, but will add my 2 cents. I wonder if this is a mental thing where your mare is so good at these difficult exercises requiring a high degree of collection, so she just isn’t sure that you really want her to stretch out? I think she’s anticipating your request to collect or to do other specific movements that you mentioned. Because you say she’s using her body correctly and obviously has skills, my approach would be to work on her extended trot, on the straights (not working renvers and travers). If she falls apart by rushing I would actually press her forward like that was your idea and keep going. I wouldn’t add anything else in this mix, just let her “fall apart on the front end” and trot on well forward. I know, it sounds so sloppy. You aren’t going to lose what she already does well. But if all you do is press her forward at trot, and more forward at trot, she will not be able to anticipate what (collection or presignals for other exercises) you may ask next and once you do get her to stretch forward then you can clean it up and put her in a frame at it. Get her doing it first, if that makes sense? You can make it more correct after she consistently gives the response to lengthen. Then you can make it pretty when she does it. My guess is she’s a powerful horse who finds collection easier than extension, or more fun because it is easy for her and you have encouraged it. Can you do something else to keep her interested; maybe work someplace different? My inclination would be to take her for a ride in a different environment she would enjoy where you can do a lot of straight-line work that she won’t think is such work in a different setting and trot most of the trip, only focus on going forward. If she offers a fast to very fast trot, I would take it and ask for more of it. I’d also start asking her to do other things you do not normally do to keep her mind engaged on what you’re asking. I would look for things that don’t involve much turning and that move her forward but you could also try trot poles to lengthen her strides. Thanks for adding your cues info; I would work on lengthening without the half-halts. Give more rein and if going deeper in your stirrups is not working, try putting more of your rider weight on her back. Sometimes adding a weight cue will help a situation like this. You didn’t say what bit you’re using but if it has shanks and is not a double bridle you might also drop back to a ring snaffle or kimberwicke to stretch her out for a while. If you’re already using one of those however, I would keep using it. Just my thoughts.

Only ask her for 2 or 3 strides at a time.

Ask for her to lengthen, and then when she does make sure you immediately ask her to collect again so it is your idea. Then ask her for it again soon – as soon as you think she can handle it.

Gradually ask her every couple strides, and hopefully she’ll be able to lengthen for longer.

Now, I have very little dressage experience. I’ve done training level tests on my horse and gone to some fun training level clinics, and my aunt is training her horse in dressage – but I’m a barrel racer at heart. But a show jumper fixed a problem with my barrel horse, by telling me what she would do if her horse was having similar problems.
So I figured it’s worth a shot!
Good luck!