I nearly cried reading about the brushing and shampooing.
Your DD's hair is dry (frizz) and if curly (very probably) Does. Not. Need. Brushing. Ever. As this will cause frizz.
Lots of conditioner. Maybe try a deep conditioner to start with (leave on for half an hour under clingfilm). Make sure the conditioner is silicon free - this just means it will be water soluable so will wash of with water and not build up. Silicon shampoos coat the hair....which then needs a strong/harsh shampoo to clean - which dries the hair.
When you condition really squish the conditioner in. Cup the hair from the bottom and squish and pulse it so you get squelchy noises. This forces/encourages the conditioner to get into the rougher cuticle of curly hair.
Only comb (wide tooth comb) when wet or damp. Never when dry.
And yes - try a basic mousse or gel - comb or rake through when damp. Leave to dry. The product helps keep the hair defined/stops frizz and kind of seals moisture in a bit. Once it dries it will be crispy....this is GOOD. Just gently scrunch out the hair (cup in hands and gently push to the scalp) and the crispiness goes.
You don't need to use expensive products. But they do need to be curly friendly - so nothing silicon and nothing with harsh sulphates or alcohols. You do not need to remember this - but just find the list of ingredients on line, cut and paste into www.curlsbot.com/ and it will tell you if OK to use.
Cheap works - especially when you are starting out. See if it improves things - and then you can maybe amend/change if you need to.
And for both conditoner and gel use more than you think you need. Curly hair sucks it up. You need it to be squishy
Cheap conditioner:www.boots.com/alberto-balsam-coconut-and-lychee-conditioner-350ml-10301683
Cheap gel - readily available:
www.boots.com/wella-shockwaves-ultra-strong-power-hold-gel-200ml-10085144?cm_mmc=bmm-buk-google-ppc--PLAs_HeroCompare--Toiletries_Men-_-UK_Smart_Shopping_Toiletries_Men&gclid=Cj0KCQiAieWOBhCYARIsANcOw0wghDvdEChvmYBrrLGoOmIxaba-nC4Uz0rYmSZiZbZ-ud342CV0CkUaAoUsEALw_wcB&gclsrc=aw.ds
If you feel you do still need to use the H&S for her scalp (though you may find less drying routine solves and scalp issues) then coat the length of her hair in conditioner before using the shampoo on her scalp.
PIneapple hair overnight (high pony tail) so it doesn't get ruffled on her pillow. And yes, silk or satin pillow case also helps prevent ruffles.
Good luck.