Hi
Having bilingual children and probably read all the literature available about raising true bilingual children (2 parents 2 different language from in utero!)
I can assure you that children learn a lot from children.
There is no point of having a group with a few english speaking kids and a mandarin teacher because then this is not total immersion but teaching mandarin as a foreign language. So the kids will leatn a few songs and hello, goodbye etc. But wont learn the language and culture because they wont play between themselves in the language.
For ex: whatever games or book they learned/read in english, when left to their device my children will play together in english if they are playing/reading that game/book. But, i saw the other day them playing a french game and they switched completely in french during the time they play the game (they are 4 and 2.5 yrs).
You said you wanted multilingual children, if you want to achieve that this is what you need to do: find native mandarin speaker who wants their children to learn this language too (and maybe a couple of english dpeaking so they can pick up the language.
For instance, a lot of native will go to mandarin school or french school on saturday.
I would be interested in a mandarin playgroup so long there are children with native parents. (This is why my kids dont go to çlub petit pierrot, when we did the trial there were 3 english speaking children for 1 french).
Good luck and keep me posted please. Sx