It's heavy on bureaucratic terminology (i.e. long name for the form titles), but it seems more or less fine. Nice job with the translation. The only part to clarify is the 'apply for it' --does the 'it' here refer to the 'comfortable pregnancy service?' We would probably say 'at the institution' instead of 'in the institution.' I assume this second form has to be filled out at the center/institution (on-site) after bringing in the first filled-out form. Since you use 'community center/public health center' I would continue using the term 'center' throughout and not 'institution.' You can also capitalize the words in the form title to keep it clearer; having the form title in quotations may be optional depending on what style conventions you're following. Also, for punctuation: "comfortable pregnancy." With the period inside the quotes. If I had to re-write something like this for clarity, I would say something like: In order to apply for the integrated service called "Comfortable Pregnancy," visit the community center or public health center. To the center, bring a completed "Health Insurance Pregnancy and Childbirth Medical Expenses Payment Application Form." Then, at the center, fill out the subsequent form called the "Integrated Processing Application Form for Pregnancy Services" in order to complete the application process.

Thank you so much!