Sounds like possibly the older girls and their parents might be, though they'd never admit it, worried that this much younger girl will either outshine the older ones -- or, if she flounders at all, they're worried she'll take up too much of your time and energy and take that time and energy away from the rest of the squad.
Sounds like possibly you have some unspoken concern here that you'd lose her to another older squad? Is that behind even a little of the desire to put her with your current older girls? You mention that you need girls and can't find them. Or are you a bit worried that if you don't put her on your squad this year her mom will say no to your squad next year and take her daughter's talents to another coach's team?
Whatever the reasons behind everyone's stances, give the kid a year to be the top dog and the best one on the younger squad instead of making her the "little kid" on your current squad. In a year she'll be older and legitimately able to join the older squad. Just because the rules say you CAN put her on your squad now does not mean you SHOULD do it. And though no one's social development will be horribly permanently injured if she's on the squad with older girls....There can be big social and maturity gaps between seven-year-old girls and 10-year-old girls. If her mom is really looking out for her interests, I would hope she'd want her girl on the younger squad for this year so that the girl has another year to mature, rather than throwing her onto the older squad solely because she's so great. She may be a great cheerleader but she is still a seven-year-old child whose interests and subjects of conversation will be poles apart from those of 10-year-olds.
Also, why wreck relationships with kids you've apparently coached for some time, just in the name of getting this one child, however good she may be?