Here are some ideas for easy baby- and toddler-friendly day trips (max. car journey of 1 hr from the centre of Glasgow). We'll keep adding to this as time goes on, but please do send us your ideas.
Finlaystone Park
Just 25 minutes' drive west of Glasgow lies this well-equipped woodland park, which contains a good cafe, several great play areas, and fun wooden adventure structures, including a 'pirate ship', wigwams and a Celtic 'maze'. Several picnic areas contain equipment for barbecues.
Finlaystone website
Inchmahome Island
Tiny island in the lake of Menteith. There's a tiny ferry which runs regularly from April and September from the Port of Menteith. Just show up, and a ferryman will take you over. You can then agree what time you'd like to be picked up. It's the perfect child-friendly trip - lots of variety in short bursts. The ferry takes about five minutes, and you then have a 15-minute walk to the other side of the island. There's the thirteenth-centry Inchmahome Priory to explore, and picnic tables (and loos) at the beach on the other side of the island. The route to the beach is not buggyable, however, so you'll need a sling/backpack.