My father went to Thai embassy in Shanghai for a TR visa before covid time. They ask for a lot of documents, including invitation letter and inviter house paper or land paper. There is visa agent at embassy. They ask quite a bit of money for a TR visa. ¥1000rmb up. So just visa exempt plus 30 days visa extension total of 60 days at the end. BTW he holds an Australian passport.
Base on your questions. Firstly, not recommended to travel with a 2 yrs old baby at this time. Second there are limited hotels to choose for quarantine, and needs to be on the list of those qualify hotel. Hotel fees will be around 50k baht depends on the hotel.