Hello- my family and I are looking to travel in China for 6 weeks next month. There are 2 adults and 3 children ranging in age from 10 years to 4 years. Ideally we would like to travel mainly via train and wanted to know if there are child discounts, are there rail passes that we should look to getting.

We intend to fly into Beijing and out of HKG. Travel in between we are fairly flexible as to where we go but intended to travel roughly from Beijing to Zhengzhou to Xian to yichang to shanghai down the coast and travel west to Guilin and then back to Guangzhou to our final departure point of HKG.
Do you think that this is very ambitious in 6 weeks and any suggestions that you may have would be welcomed.
thanks