Take her. Let her meltdown if that’s what she wants to do. Then tell her she’s still getting the needle. I sit my son on my lap. Cross my legs over his body. Take one of arms and cross it over both of his arms. I use my free arm for extra support. He gets his needles and he’s a hefty little guy.
My youngest son (6) has Down Syndrome and we've struggled with doctor appointments, shots, blood work, bed time, brushing teeth, etc. We do our best to treat him like a typical child at his mental age, not his physical age. Sometimes it takes a while but we have to make a routine and keep him to it despite him wanting to or not. He tries to be sneaky and get out of things, but with a firm voice he will listen. As for doctor appointments, I really have to thank the nurses and doctors for being patient with him. They'll talk him through what they are doing and ease him into it. Sometimes it works and sometimes it doesn't. I try to make his appointments at a time of day he'll be more cooperative. If it has to be at a time he might be tired then I try to get him to nap before. We try not to make a big deal about it. Don't get me wrong, I do handle his fits and melt downs differently because he's non verbal and most of his frustration is he can't communicate easily.
I don't really know if I want or can use force.. she's literally an inch taller than me and my size. I understand tho that I have to always mean what I say and not give in just because of meltdowns. I'm doing better with that. I just think she feels so strongly about this particular thing that I don't know if she will budge. I want her vaccines done pretty badly tho. I think I just must find a way.
How much do you want it done? If you teach her she can control the situation then she will. You have to have balance. You want her to feel in control of somethings (what she wears, what she eats, etc) but you need to choose your nonnegotiable issues and stick to your script. If meltdowns get her out of doing things she doesn’t want to do, then she’ll use that method because it works. Either ur training her or she’s training you. Bed time will sort itself out. Remove all electronics, turn the lights out, if she decides to stay up then a natural consequence is being tired the next day. That’s her choice. Going to the doctors is not her choice. She’s 11. Even neurotypical 11 year olds would take advantage of your flexibility in this area.