Go to your great grandmother's funeral. Just say she was your Grandmother and part of your immediate family. (Even though I consider great grandmothers part of immediate family.) If they raise a stink and they and talk you out of going, just say when you'll be back to work AFTER the funeral. Kroger IS ABLE to handle some things BY THEMSELVES.
Go. Just go. Family is more important than work, and there are some managers who do realize this. If they don't, that's on them, but you'll always regret if you don't go.
You get three days funeral pay and it is a very reasonable accommodation to take a brief time off for family emergencies. Keep in mind that you also get two days no show pay for a brief absentee. Just show up on the third day or your job is at stake. You can also request a brief leave. This will be unpaid time. You can also use your vacation pay to supplement the income. If you're struggling with the mourning process get a doctor's note that states you're emotionally struggling then request an ada reasonable accommodation. I wish I did that because I didn't understand because I kept flipping out on customers b.s.ing over cents.