THe fact that it is pinned, that it is in a hoop, and that the stitches are inset and in a perfect line, suggests strongly that she was in the quilting phase. I think if I would hand quilt something, I would probably end up with large stitches (as I am not practiced, nor patient when it comes to hand work)
You have choices.
You can continue in the same style and finish the quilt.
You can share the quilting with your mother and make it a 3-generation quilt.
You can take out the 10" and finish it on the machine.
You could even send it out to be done by a longarm quilter.
EIther way, it will be a wonderful memory of your grandmother and you can be very proud of yourself that you are tackling this project.