Temporary Chinese passport (One exit one entry) for a Child born in China with Foregin father

Dear
I have a daughter born in China (Chinese mother and Sweden father) My daughter has just recieve a Sweden Passport. Now we would like to visit Sweden this summer. As it will take to long time to apply a Chinese entry permit in her Sweden Passport, we have been informed that we can apply a temporary Chinese Passport, witch she can use leaving China and come back again. So now my question is folowing. Will it be any problem to leave China without any Sweden entry permit in the Chinese Passport. I would assume she can use her Sweden passport as VISA for Sweden.
Will it be any problem if we show her Sweden passport in the customs as she have two passports and China only allowed one citizenship. Thank U