If your mother's illness is proved by the hospital to be covered by the additional major illness policy, the insurance company will unconditionally cover it. If you suspect that the insurance company is deliberately making things difficult, I don't think this will happen. It is part of any insurance company's job to deal with claims. As long as the cases reported by customers are within the scope of protection, claims can be settled. I don't think the employees of any insurance company want to delay and let a case know as soon as possible. If you don't quite understand what documents or certificates the insurance company needs to provide when handling claims, you can call the hotline of Taikang Life Insurance for consultation first. After all, it is not only annoying to run many times without providing complete business information, but also delays the time of claim settlement.
I wish your mother a speedy recovery!