Can I complain if I don't have an ID card to go to Home Inn?

You can complain, but it's no use. You can't stay in a hotel without an ID card. If you complain again, it will be unreasonable.

Chinese mainland citizens who really need to go through the boarding formalities without valid identity documents shall declare and verify their identity at the local police station. The police station can print the information of the passenger in the national population information database, and affix the official seal to the passenger as the proof document for handling the flight formalities.