Train from Muslim Hotel Shenzhen to Springtime Hotel Guangzhou.

Many trains run for the journey and I don't think it is necessary to book the train tickets in advance. Just buy the tickets on the spot!

For the directions between the two hotels, here is the way (Springtime Hotel has two branches and I assume you refer to the one on Xinyan Mansion):
take a taxi from the Muslim Hotel to Shenzhen Luohu Railway Station at a cost of CNY10. Take a bullet train from there to GZ Station within 1.5h. Then take subway line 5 to Ouzhuang and transfer to line 6 to Yantang. The exit C is only around 320yd to your hotel.