What Are Grandparent Rights, Alabama

Hi! I 27F I do not talk to my parents due to previous emotional abuse/manipulative behavior, if it is relevant I am happy to explain more. When I went no contact 4 years ago, I made sure they didn't know my address or phone number. They do not know my fiance and our house/phone plan is under his name. I cut off basically everyone who I felt like could talk to my parents out of paranoia due to previous behaviors (stalking, hiring P.I., guilt tripping, ect).

Recently, I got an email from my parents saying that an old friend of theirs saw me in the grocery store and congratulated them on my pregnancy. (My parents tend to keep a public face, so I am sure other than their close friends no one knows I am non-contact.) They demanded more information and to be there when my child is born. They told me if I deny them then they will go to court to get visitation rights or even full custody. I know they would have no grounds for full custody, but after looking at Grandparent Rights I am confused if they can legally see my kid. I am not that adverse with legal jargon.

I am currently 29 weeks pregnant and will see a lawyer if needed, but I also don't know if they are bluffing or not. I rather save money due to needing a c-section, any unforseen problems early on, and just children being famously expensive. I can afford a lawyer if needed, but I am uncertain if this is something I should even be worried about building a case over.

I am trying not to stress since I have a high-risk pregnancy, but my parents having influence over my child is very worrisome to me. Is there any advice or information anyone may have regarding this? Thank you all in advance!

Location: Alabama