My daughter and I share an apple ID account. I have an iPhone and she has an iPod touch. The songs that I have purchased for my phone go onto her iPod and I can't play them on my phone.
Welcome to iMore! When you say that you can't play them on your phone, are you getting an error message? What exactly is happening? I'm assuming that your daughter has automatic downloads for music turned on in Settings > iTunes & App Stores.
If you share the same iTunes ID, you should both be able to download the same songs or different songs. Why can't you download them. My Wife and I do that.