Hmm, couple of questions what type is your mare, WB or TB or cob or native? What are your aims with her, do you want to get to higher levels in dressage or more just want a nice safe fun all-rounder that's been correctly started? And does your instructor mainly only ride her own horses or is she experienced in producing youngsters for the amateur/leisure market?
The thing is with young or green horses it very often is one step forward and two steps back, when you are teaching them new things or trying to correct faults (which can be the case even with youngsters, if they have a confirmation fault or just a just a naturally incorrect way of going) sometimes tension will creep in if they are confused or resistant, it can't always be totally avoided. I wouldn't have thought it's a mare/gelding thing particularly, just a personality thing, some horses are stressier learners than others. A good rider should be able to school them through it in a kind, non forceful way, but that doesn't mean never asking the difficult question if you see what I mean. The reason I ask whether your instructor is used to producing horses for others is that IME pros when producing a horse for themselves or the professional market in general do often ride in a way many of us would find more forceful and directive than we are used to and different to how we would ride ourselves, it's not that it's wrong per se but it can then be confusing for the horse to swap between the two styles of rider so although the pro may get great results sometimes if you just want a horse to have fun on for yourself it may not be the best choice.
Either way, if she's such an amazing teacher and friend I would have thought she should be happy to explain to you what she's working on, if/why your mare is finding it difficult and causing tension, and what the plan is to correct. Different situation but my current older loan boy tends to be very hollow when tense, I'm constantly trying to get him to relax, I was surprised when his owner got on that she wasn't actively trying to get him to soften, if anything she seemed to be exacerbating it by taking up a really strong contact - she explained to me that part of the reason for the hollowing is his lack of straightness so it's important to correct that before worrying about where his head is, so she worked for a good 20-30 mins purely on straightness (he's stiff so takes a while), which he was a bit resistant to at first, but when he eventually loosened up he did also then relax into the contact much better and also was working more correctly overall - she and I were aiming at the same thing but taking different routes if you see what I mean?
I think a general, non negative conversation with her about how it's going would be a good first step, like I say any reasonable person would be happy to explain their methods and rationale (doesn't always come easy to a horsey person who may think it's self evident what's going on of course, but it's an important skill if you charge for producing/schooling horses for their owners!). I think on the whole if you do want to back out of having her ride the mare that will be natural enough, presumably it was never intended to be a forever arrangement, only while she's being brought on, and if you are happy she's now going as well as she ever has without instructor needing to ride, then that's the obvious answer about why you don't need her to ride any more. Shouldn't close the door to her restarting in future if ever needed? Lessons are a different thing, and again if you are happy with what/how she's taught you in the past why not keep having lessons even if she doesn't ride for you any more? Or just quietly book with someone else and if asked just white lie say the times/locations available from the other teacher were more convenient or your friend wanted someone to share with or you wanted to do more jumping and you know dressage is other teacher's thing or blame the cost of living or something along those lines (I've recently dropped a teacher who I tried out as an experiment but just wasn't digging, using exactly the cost of living excuse, saying I'm not having many lessons any more even though that isn't strictly true, I am still having lessons just not with her 
). TBH even if what you say is 100% right and instructor just doesn't get on or understand your mare, if you say that it will absolutely come across as personal criticism of her so I'd avoid that!