It's a very personal decision.
My mum cane with us to the hospital (she drove) and brought a book with her as she expected to be kicked out at some point but would stay in the car/corridor to support DH (overnight labour, we were knackered, no men's loos on labour ward so he had to leave a couple of times).
As it was she stayed throughout and was fab. She fetched midwives and cold water, kept out of the way for most of it, held my hand while I was stitched and described DH holding DS as I couldn't see them. She was also great for explaining my medical history to the mws and, when stirrups were brought in, she explained calmly why I couldn't use them (hip condition, they'd been ruled out by consultant). She even cut the cord, with my permission.
After the event she has said nothing but how strong and brave I was to others and stepped away to give us some space without being asked.
She was, frankly, amazing.
Not every mum is in that situation, and DH and she have a fab relationship, which helped, but the decision is yours and yours alone.