The parents provided this playpen and no, it doesn't have velcro unfortunately. She only naps once a day unless she falls asleep in the stroller on the way to or from the park, but sh esitll tries to flip the mattress at least once before sleeping. It isn't as bad when she doesn't sleep in the stroller, so I wake her up as soon as we reach our destination. However, she still does it a bit. Hopefully it will stop with time.