Dear J.,
You have already had some great ideas offered. You didn't say how old your daughter is. Honey is only ok if they are over 1 year of age.
Some things that thin mucus- as was written, no milk products, however breast milk is great. You can make a gruel out of Slippery Elm Bark with some warm water and I like to add honey with a little cinnamon to taste. It is quite nice tasting and helps lessen the mucus. Just feed her a few spoonfuls three times a day at least. Also Fenugreek in a tea form or tincture is very helpful. I have many times boiled honey with onion diced up in it. I would then strain it for a cough syrup- the taste is ok and the kids don't mind if you don't make a face or fuss about it! Lessen her meat intake for a while- it also increases and thickens the mucus production.
As mentioned, you can take her into the bathroom with a steamy shower- when patting her back, cup your hand to make a percussive sound on her back- like a clap. Work your way back and forth across the lower ribcage then up a little and across, back and forth- repeat the pattern back and forth to the upper back, this also is very effective in loosening the mucus from the lungs. You'll get the feel for it, it is firm, but not a slap that hurts. This can be repeated several times a day....and always keep her really well hydrated- that, in addition to the humidity is probably the most effective in getting the mucus mobile!
God Bless,
H. B. MOM (mother of many-9)