Finger comb her hair very gently in small sections, brushing is for straight hair, you won't ever be able to easily run a brush through your daughter's hair and you don't actually need to. Many curlies do not brush their hair ever, do not comb even daily, some just finger detangle in the shower and at no other time.
Avoiding or limiting tangles is about the right products, techniques, overnight care. Looking at your daughter's end of day photos I don't think you are using anywhere near enough conditioner or not a truly moisturising one (ignore the strapline, consider ingredients). I would not bother with stylers like gel or mousse, you can conditioner-only style.
Kids don't produce sebum or sweat like adults do, if you are not using silicones that build up they don't necessarily need shampooing, you can either conditioner only wash or pre oil overnight then shampoo. This will strip and dry out the hair much less. There are videos on YouTube of parents caring for their children's naturally kinky coily hair using the CG or Tightly Curly methods.
Kynnedy Wash Day: How to Wash you Princess (TODDLERS) Hair with no Fuss! - YouTube
(part of a whole series)
There are also children's curly hair products, I believe the adult CURLS line is available in both Walmart and Target now, I am guessing their kids range Curly Q's is too, that whole line is Curly Girl friendly and originally designed for kinky coily hair. If you like it you can get 32oz bottles on the CURLS website. Curly Hair Care Advice | Curly Hair Products & Natural Hair Care Products | Shampoo, Gel & More
The Infusium 23 leave in is little more than silicones it's not moisturising, it doesn't actually contain much in the way of true conditioning agents like cationic surfactants and fatty alcohols. You might be best purchasing a regular creamy type conditioner and using that as a leave in. In the short term the Infusium 23 regular conditioner you have is better than the leave in.
Please don't put a relaxer, a texlax or a keratin 'treatment' on your daughter's hair (I can tell you don't want to anyway). These contain harsh chemicals that have no business on a child's delicate skin or hair, don't believe any stylist that tells you anything different. I've heard horror stories of kids younger than yours who have already started with hair loss on their edges from being subjected to adult treatments and adult styling.