Hi, I don't have all the answers for Mandarin resources but I can encourage you a little! It takes a bit of organisation on my part to get foreign languages factored in each day but it is well worth it & slowly but surely you will see results.
We are bilingual (Eng & Spanish) & introduced French as our 3rd language -
Little Reader French: so far this has been our biggest expense, so not too bad
Youtube cartoons (Petit Ours Brun, Oui Oui, Sam le pompier), songs & clips (numbers/ days of the week/ months etc). Any cartoons that my son (age 4) gets to watch are always in French. He thinks it's such a treat to get to watch something that he doesn't care which language it is in
Librivox (free) have some audiobooks (books in the public domain) in French. Max et Mathilde series comes with CDs, & I have a French encyclopaedia with a CD that is useful.
International children's digital library (ICDL - free) has loads of books translated in & from many languages. On occasion you will be find that a book has an audio version there too.
We have a French Alliance chapter in the city which I hope to make good use of in the future.
4th language for us is a local indigenous language, Kuna. This we learn by having a native speaker in our home for several hours a week. I think this is the ideal way to learn a language. But... for the one we picked it's a little slow going (for me probably more so than my wee boy) since there aren't too many resources, written or otherwise, to augment our study.
Then we are starting Greek. I plan on following a course to give us some structure but that will obviously incur costs. How long or how far we pursue this I'm not sure, it will depend on how much my son enjoys it. We are learning the alphabet for Daddy's birthday to hopefully convince Daddy that Greek is a good idea
ICDL even have Greek books plus their translation in English but no Greek audio unfortunately!! I like elements of the classical education so Latin is also on the list but then that's definitely it for languages:-)
All the best! Lois