I need advice. Anyone can input!😬

Destiny
Okay, so I'm 37 weeks and 4 days. I recently found out my grandma was diagnosed with stage 4 lung cancer. It's progressing a lot faster then we thought it would. She also had gotten a blood clot from the IV she had from being in the hospital. They're concerned about the blood clot going to her heart. So she's been put on blood thinners, but there's a change that they won't work. Or make it worse. I'm afraid she can't under go surgery either because her whole body is weakened by the cancer. The doctors gave her 2 weeks tops to live. And if she does survive past the expectations, she'll be starting chemo. Which means she will not be able to be around pregnant women or babies, due to the radiation. Literally the only thing that gives her hope and makes her day turn from horrible to happy is the thought of her getting to meet her first great grand baby.. And this is where my dilemma is. I know I can't control when the baby wants to come. But I so badly want my grandma to meet him.. That's the only thing that brightens her day, and it's pretty much her last wish. So I was thinking about talking to my OB about induction. I'll be technically full term this Friday, being 38 weeks. He said the earliest he'd induce anyone is 39 weeks. Which is perfectly fine. But I still haven't talked to him personally about it. If he did say it would be perfectly okay and my baby was healthy enough, should I even consider? I'm not trying to seem selfish or rush into labor.. But my grandma is literally dying. And she may or may not make it until he is born. I wouldn't even be considering this if the doctors didn't put us on such a short time period. I need advice or an opinion. What would you do if you were in my shoes?Â