Induction -Long post sorry. Need advice

Okay glow I have a question. So as far as me being high risk. I can’t go over 39 weeks. I’ve had a previous stillborn and they feel it would’ve be safer to get baby out at 39 weeks. Which is cool with me. I will be 38 weeks this upcoming Sunday. I have my weekly nst and 38 week appt Monday morning. Which is where she will set the induction date.

My question is, is it likely she will set it for that Friday which will be the 31st if I ask? Or does it HAVE to be right at 39 weeks which will be that Sunday .? I ask because I don’t have much help family wise. I’m a single mom of three. And my previous baby’s dad is deceased. I’ve gotten my moma to agree to watch them while I give birth since we know how many weeks I will be when the time comes. The thing is I live In a whole different area than my moma. My kids go to school in the area I live in which isn’t close to my moma at all. My moma also has to work! And she works during the day. She will be able to take my babies to school but not pick them up cause she will be at work. So I just wanted to know if y’all think she would be okay with letting me go at 38+5 since it’s a Friday. Which means it’s the weekend. My mom won’t have to worry about getting the kids to school and figuring out who will pick them up or any of that. I’m trying to make it as easy as possible for her since she is my only help. I havent brought this to my doctors attention yet cause I literally just thought about it at 3:30 am. I’m woke due to having to pee😂😂😂 plus my doctor only delivers at my hospital during the week and another during the weekends and my insurance does not cover the weekend hospital. I don’t want the on call doctor delivering my baby I want my OB so I also feel like friday would be a perfect time. I never have labors for over 12 hours. So I think I’ll fit right into the time frame for her to deliver before she gets off for the weekend. What do y’all think