I had my mum & dad in during my labour with DS1, although ended in c/s, so was just DH for the delivery. I don't know if mum would have stayed for the delivery otherwise, I know my dad wouldn't have done (he rushed outside every time they did an internal). It was a long old slog though, so they provided relief for DH. After my c/s, I was a bit ill, so my mum stayed with me whilst DH changed out of scrubs, saw DS1 etc. Tag team worked well. They held DS1 whilst I was transferred to the ward and sorted out. They all saw DS1 having his first feed (my youngest sister was there too by that point!). It was all lovely. Great photos and memories of DH and my dad in Who's the Daddy? and Who's the Granddaddy? t-shirts. (arriving at hosp to birth - 12 hours)
With DS2 my parents lived in Cyprus. Again, long drawn out affair. My mum managed to make it from Cyprus between waters breaking (Sun night) and DS2 arriving (Sat night)! My youngest sister looked after DS1, and my middle sister and mum visited me whilst in labour. They then went home. When the induction/augmentation seemed to be not working, and a c/s was called for, I asked for my mum to come in again. She did, and supported me for a while so DH could have a break. DS2 was eventually born naturally, and my mum was there for all of it. It has traumatised her a bit I think as it ended badly (DS2 crashed at birth, went to SCBU, but is fine now). However, her support was great. DH went with DS2 whilst I had a bath, got stitched up etc. Another tag team effort. They both got me settled in the room before leaving together. (arrival at hosp to birth - 52 hours!!)
It really depends on how it goes, but if it gets long like my labours did, I think having two (or more!) people is a bonus for the person in labour to feel fully supported the whole time.