Dear aangeles,
I didn't know about the free music CD but I'm so happy to know that there is one. May I know where you studied in Manila? If you don't want to tell, it's alright.
I myself cannot speak Mandarin well so I am currently listening to the Chinese Pimsleur audiobook. Though the CD is more appropriate for travelers, it still helps me practice speaking Chinese inside my car without getting embarrassed.
Actually, Mandarin is not my first language either. I grew up speaking Hokkien with my family and Filipino with our helpers and the community in general. However, since it is nearly impossible to find children's educational materials in Hokkien, I decided to speak to my baby in Mandarin and teach her Mandarin instead. I must admit that my Mandarin was quite rusty and I actually had to run to the computer to use "Google Translate" quite often in the beginning. I went to Uno High School in Manila and terms like "diaper" and "wipes" and "building blocks" were not exactly included in our chinese textbooks...
It has definitely gotten easier over time and now it actually feels unnatural for me to speak to my daughter in any other language. So I would definitely encourage you to keep learning and practicing and also teaching your child.