Corrieri’s is very good for a quick meal, but for me it would be to far off-route.
Highland gate is a chain pub type place, right next to the motorway & has baby changing, play area (inside & out), so is really family friendly. We have only been once, but I think it would be my choice at Stirling. https://www.highlandgatepubkildean.co.uk/
Tiso at Inveralmond roundabout in perth has soft play and a good little cafe, we are probably there about once a week (with a 2.5 year old). I’m not sure if the opening hours for soft play (tiso tots) would suit though & it would probably be unbearable to take a toddler for food when the soft play is closed.. https://www.tiso.com/shops/perth-outdoor-experience
There are also quite a few good little cafe’s only a mile or so off the A9 in Auchterarder which I could recommend. Cafe Bianco is our favourite for a quick family dinner out http://www.bianco2go.co.uk/ but there are a quite a few.
BTW, Happendon services on the M74 is now owned by the same people at Tebay & Gloucester.
HTH