Dear Olayan,
Greeting from Peggy, Top China Travel. Thanks for visiting our site.
Here are some suggestions for your reference
1. 20 Days tour in China just within $5,000 for 2 adults + 2 children may be a little unreasonable. Accoding to my experience, tour within 13 days may meet your budget better. Exactly price may be various based on different destinations.
2. And according to your travel time (late June), we have designed some tours which are suitable for travelling in summer days. The following link is for your reference: /china-tours/china-summer-tours/
3. A thing should let you know that the "housing in apartments contain a kitchen" may be not a general arrangement from us. In China, this kind of apartments may be less for renting, and also not recommend to travellers. Generally, for buget travellers, we can arrange 3 star hotel with English speaking staff which may ensure the safety of our clients.
Hope above information can help you.
Feel free to contact with us in any moment by mail if you have any question on China tour service.
Peggy