You are right, you can't change the decision. Also, I think that the option wasn't offered to you because of your DD's age. Here in Australia a palate expander is fitted much earlier age 9, 10 or 11.
So here is our experience (for anyone who is making decisions about teeth...)
My eldest (now 12) has a narrow face (like his father). He had severe overcrowding with his canine teeth sticking almost out parallel to the ground etc and he also has a significant (12 mm) underbite.
DS had an expander fitted in early 2017, just before he turned 11. The orthodontist asked me to do 1 'turn' (which slowly expands the upper mouth) each night 25 times. No 'turns' for a few months and then late last year another big series of 'turns'.
His upper jaw has now been expanded to have room for all adult teeth. His lower jaw grew in width to match it.
So the result for him with a palate expander has been that DS now has no crowding and we have AVOIDED braces! Fantastic - the overcrowding is gone. All his teeth are aligned and there is a little bit of space.
Last week we had an assessment for the next stage which is that huge underbite. He is going to have 'blocks' but we don't start that until December.
My DD (now 10.5) also had a palate expander fitted last year. Hers was glued in when she was 9 and a few months. She has needed less 'turns' than her brother. Again, DD now has room for all adult teeth. She has unfortunately inherited my DM's 'horsey' (protruding) teeth so will need braces either in 2019 or 2020.
Both my children still have their expanders still glued in. They are left in to keep it all stable.
I recommend palate expanders, but I think you need to get an orthodontist to assess them much earlier than for braces (Year 3 or Year 4) so that the orthodontist can get the device in and start working on the size of the mouth well before the child starts the big growth spurt.