What about hiring a tutor to coach younger daughter through the aspects that make the GT program tough?
Aside from the tutor not being mom so she likely wouldn't yell at the person and cry

, what do you think we could get out of a tutor that I couldn't do myself?
Jumping in rudely here -
Not much (except maybe the inside scoop at the school), but do you want to do it? You are a good parent and probably interested in her divergent thinking and unique approaches and on some level you validate them. A teacher familiar with the curriculum might be more able to execute a teach to the test approach with her. Obviously not your long-term goal for your daughter intellectual development, but just a short term crutch to give her confidence.
It may be very different at your daughter's school, but I find it very hard to get info on assignments or expectations beyond what my son writes down in messy writing in a tiny space in his agenda. Also, they have no real math or grammar textbooks. So I might get the info that they are working on predicates, but that is it. I usually never see any of the work. So while I am certainly capable of presenting predicates to him (well, after I google it a couple of times) I would not necessarily be able to efficiently prepare him to take his teacher's test.