"OOO I forgot, she does have a pair of goggles that aren't tinted. I think that would go over well "
Honestly, I know you are being silly, but for synchro I think goggles might actually be safer. I skate in glasses (can't see a darn thing without them, I'm worse than 20/200 uncorrected) and really only have problems that they fog up on some days (and if I don't have a backup pair of contacts I just have to leave- I can't wear contacts regularly due to a medical condition, so I buy 1 box of dailies at a time, and wear about 20 pairs a year)) and while they very rarely fall off, they have before. I skated synchro and I'd be terrified someone would trip over fallen glasses, and either hurt themselves, or crush my glasses. In singles skating, you put yourself at risk, in synchro there are a lot more people to worry about! You should definetly consider sport glasses.
In synchro the rules don't even let you wear bobby pins in your hair! It's possible the team is interpreting the rule about ornamentation, since sunglasses are generally considered that, and not the same as regular glasses. In which case, it only says it needs to be firmly attached to the head, and a behind the neck band should do it. But I do agree it will look ridiculous to have one member of a synchro team in sunglasses, so the coaches might just say no way.
One thing I'm not clear about- is the tinted lense thing a TEAM rule, or a COMPETITION rule? (As far as I know, it is not a federation rule for either ISI or USFSA- but you could try emailing them too, I've found both federations to be responsive.) In addition to federations who make the overall rules, competitions can set their own additional rules, and teams can have team requirements. (Some teams do not allow haircuts during the season, for example. That's certainly not a federation rule.) If it is not a federation rule, since it is a beginner team, you could better petition the right people- if it's a competition rule, the team can't help you, you need to talk to the referee. If it's a team rule, then you could ask for a one time exception, and then remove your daughter from the team.