transfer to other school - how are covered the 2 months holidays over the summer

Hi,
My situation is simple. I'm an ESL teacher ready to transfer from a school in a province (Hubei) to a school in another province (Guandong). My contract & residence permit are valid till the end of the year. I convinced my school to agree to let me leave ("didn't pass the probation period") at the end of this term, without paying a breaching contract penalty. I was told it's better to find a new school before end of June (end of term) so I did.

So my question is: when transfer/ renew my residence permit - how are gonna be covered those 2 months holidays over the summer. 1st school told me they have to cancel it once I leave (from July), but the 2nd school told me that the contract will start only from September. So how can I deal with these (July & August)?

Thanks for any help :)