Since you have senior citizen and toddler, I recommend you take a taxi to save energy:
Firstly, take two taxies from Tianjin Airport to Tianjin Railway Station (Within CNY30.00 per taxi one way), then take bullet train from Tianjin Railway Station to Beijing South Railway Station (CNY58.00 per hard seat ticket; CNY69.00 per soft seat ticket), third, take two taxies from Beijing South Railway Station to the hotel (CNY30.00 per taxi one way);

Or take the Tianjing Airport Shuttle Bus(https://www.travelchinaguide.com/cityguides/tianjin/airport-bus.htm) to Bawangfen coach station of Beijing, then take taxis to your hotel~