I am a qualified afro hairdresser so I know a little bit about this lol.
Do not use a brush. Invest in a few combs. First, a really really wide tooth comb, plus a usual afro comb, then a really thin comb like a man's hair comb. It's usually useful to have a couple in between those sizes. Also good to have spares as the combs can break.
The best time to comb hair is while washing. Wash with shampoo, focusing mostly on the roots. Try not to tangle the hair too much. Add loads and loads of conditioner and comb it with the wide tooth comb starting at the bottom and working your way up to the top. Then use thinner combs until you can pass the thinnest comb through the hair. Then wash out the conditioner, gently rubbing the hair as the water passes through it. Don't tangle it if you can avoid it. Once its free of all the conditioner, use a mid size comb to comb through it when it's wet. Pat the excess water off and do the same combing.
Add a product to the hair at this point such as coconut oil, a mixture of coconut oil and gel, 'hair grease' or any other frizz-ease kind of product. This should be focused on the mid section and the ends Comb it through and leave it to dry naturally. If you blow dry, use a curl attachment on the hairdryer and do so at the lowest heat you can. If you want a different look some days, comb the hair when it is damp with the finest tooth comb and plait it into two plaits, combing as you go. When it is dry it will be wavy (providing you have combed it enough as you've gone along).
Only need to wash once a week, perhaps even less depending on hair texture. Experiment with how long you leave it.
At night, gather the hair in loose plaits and tuck under a silk cap. If you cannot find a silk cap, use a silk pillowcase. To revive the hair in the morning, use a water spray to dampen any areas you need to comb. Add more frizz easing product or oil and pull through with the widest tooth comb and your fingers.
You might also find she has a dry scalp. If this is the case, reduce washing and apply a natural oil such as olive or jojoba or coconut to the scalp by parting the hair at different points and rubbing it in with your fingers. Avoid the hairline otherwise you get a greasy look.
This website is actually a white mum with adopted black daughters but has a huge range of styles with excellent instructions. They can be used on mixed race hair too. www.chocolatehairvanillacare.com/
I advise you make hair time a really fun time. Put on some great music, watch a film together or something to take her mind off it because it can be time consuming to care for tightly curled hair properly. It's a part of her black heritage and if you can make it a great experience for her that makes a big difference. A lot of mixed race kids with white parents who moaned and complained about their hair came to see themselves, and blackness, as inferior. It's great that you're trying to make this a positive experience.
I'll find some product links now and post. :)