find a good child psychologist that does play therapy and can help you tease out what in her behavior is related to the gym situation and how to best parent her through any behavioral issues that are coming up. For whatever reason this hit her hard - I have a DD who either doesn't notice things at all (that's how she was at age 6) or takes them way too seriously (last couple of years) and she LUVS her counselor, believe me!!! (as do I). Having a trusted adult not mom or dad can help if another adult who you trusted hurt you in some manner - its not all about "talking about it" but learning to see things differently, put the event in perspective - which she can do even at her age. Some kids would have made it straight from "Coach A was really mean" to "Coach B is nice like most people and I like them much better", case closed - but sounds like not your kid (or mine sometimes).
If gym is fun at age 6 then a child should by all means stick with it. If gym is not fun at her new gym, and has not been fun for long enough to be sure its not because "suzy" didn't invite me to her party, or "I don't like the green mat and sometimes we have to use the green mat", or "I don't have the same pink leo that the other girls have", then a break is very overdue. I assume her new coaches know something about why you changed gyms and at this age "should" have gone out of their way to make sure she was in a supportive, friendly and accepting, positive environment.
Also, make sure that no one is putting any pressure on her gymnastics. She's very young, and if she "lost skills" with the change she should be encouraged to understand that is super normal and no big deal. If her self worth was already questioned because of the old coach, then the last thing she needs is any sense that being Level 2 (if I understood you right - so essentially pre-team/basics - which is totally age appropriate) "again" is a problem. I always looked at my kids job at that age (my 2 youngest were on team or team track then - like yours) was to pay attention, be nice to their team mates, and do what the coach said while not doing back handsprings in the target parking lot - whether they competed or not, whether they moved up or not, whether they had a new skill once a month or once a year - NOT in the equation....sure I loved watching them learn new stuff and was proud when they seemed to excel, but also accepting and encouraging when some things took longer.
The reasons 6 year olds are doing gymnastics have VERY Little to do with gymnastics long term for 99.9% of them, so it shouldn't be something we as parents let color their whole life in negative ways - and IMHO they, as 6 year olds, should have NO IDEA about their "long term gymnastics future" - they should all be dreaming of the Olympics whether they are working on their kip or their cartwheel at this age!