I approach cross-firing a lot differently than most people. I do not think it should be ignored. I have only seen horses get very comfortable cross firing rather than teaching themselves to do it right.
I see it as a combination of lack or strength, lack of flexibility through her spine and hind end and a pure lazy habit. It requires a lot of effort to bring that inside hind leg up to stay in that lead. It is simply a lot easier to just let it flop out of lead. When a horse does it both direction, it has never been a soundness issues with any of the horses I have worked with.
I usually teach every horse to canter/lope correctly in a round pen or on a longe line by correcting it instantly when it lets its hind end flop into the outside lead. I never accept it.
On a longe line, I will abruptly snatch it down to a trot and give my standard audible "Ah!" when I do so. I immediately ask for a lope again and let the horse continue as long as it does not crossfire. It generally takes only 2 or 3 longeing sessions to get one to where they correct themselves from just reprimanding them with an "Ah!". Within 2 or 3 more sessions, they will seldom cross-fire any more and will 'fix' it themselves without me doing anything. Since this horse has done it a lot, it may take a little longer.
I do it a little differently in the round pen. I don't let them slow down to correct it. I 'get after' them and chase them harder yelling at them until they 'fix' the cross-fire by catching up with that inside hind leg. Then, I back off and just let them lope arond. Again, they have it figured out in 2 or 3 sessions and will fix themselves or bring that hind leg up with just one "Ah!" from me.
I am not against using side-reins in this kind of situation. Would it be better to ride a horse up into the bridle and use 'true collection'? Of course! But, we have to take a rider's level of ability and have to know if a rider that is not at that level has quiet enough hands and good enough coaching to get it done properly. Side-reins are very much preferable to trying to do it with hands, seat and legs if the rider is not at that point in their own training. This is 'advanced' training and not what I want an intermediate level riding even 'trying' to do. This not a beginner or she would not know enough to try to address the problem. She would not use side reins and would not even recognize the difference in how a horse travels 'in frame' and how sloppy she is on her own.
I have watched too many people try push a horse up into the bridle and all they got done was to jerk on the reins with unsteady hands and use a pair of undeveloped legs that are out of rhythm with their hands. This rider may be an expert rider or she may be an intermediate rider. She may or may not have a trainer or coach to help her get proper collection and balance while on her horse. She will eventually have to do it as her horse will learn that she can be sloppy and work less with a rider than on a longe line, but the mare's strength, flexibility and coordination can be greatly improved in the meantime.
I would gradually get her working in side-reins with the inside rein 1 - 2 inches shorter than the outside rein which requires more bend and flexibility and MUCH MORE effort. Eventually, one should be able to longe her with the inside rein 3 - 4 inches shorter. The more she learns to do this while maintaining that inside lead behind, the better her balance will become and the more obedient she will become. I would definitely start correcting her on a longe line without side reins. Only after she figures out she is not supposed to cross-fire, would I add the side-reins.
I would also use side-reins with an elastic or rubber link in them. Obviously, this mare is well past the stage of fighting the side-reins. But, when she starts correcting her for cross-firing, she may initially throw her head up and stop herself. She will get over it and should be immediately asked to get back into a canter.
The proper use of 'training tools' is much preferred to unskilled hands at my house. We have the skill that is available to us in any given situation. People are not born expert trainers. We are all a work in progress. Many 'trainers' that make their livings training full-time are unable to collect a horse properly. I wince every time I watch TV trainers like Craig Cameron even try and most people would call him an 'expert'.
One of the other things that will help this mare is to do 'leg yielding' exercises. They really need 'eyes on the ground' to do them right, especially on this kind of stiff horse. They have a tendency to just shift their butt out rather than yield laterally 'ribs first'. A person must be sure they are actually bending through their spine. Being able to bring a horse's hip into the center of a circle (with the horse's nose to the inside) is a much more beneficial exercise, but this maneuver is even more advanced and more difficult to do, so I would not even try to go there yet.