"Family time" won't work. The need for religious accommodation MIGHT work. It depends upon whether or not your religion specifically requires Sunday attendance, or morning, etc., and if there is no way that you can adjust your schedule to attend later services (if available).
The employer may attempt to provide you time to attend services so long as it does not create an undue hardship, but may require that you work after them. Indiana, I believe, an employer may require you to work every day.
Your option is to discuss your situation with an employment law attorney. The fact is, however, that many employees attend church on Sundays. If it does create an undue hardship upon the employer to accommodate you, you would have to search for another job.