I'm not a g'ma, but IMO this sounds like a good thing. You're still in your 50s, not the frail 80s, so you can certainly handle it. It won't be for years on end.
You get to do some baby mothering, and in the best way: part-time.
Your husband may not be at ease with the tiny one, but he has been a dad before. It'll come back to him, or if he was never involved in infant care with his own kids, it's time for him to have that experience.
Realize that lots of young teens learn to deal with crying and fussy babies. He'll learn. Practice will make you both more comfortable, and you have better judgment than young teen babysitters. Besides, babies get bigger quickly, so she won't seem so fragile very soon.
It's a big help to your step-daughter, and what a great way to bond with the baby.
Enjoy!