Tracking activity while jogging with stroller

Call it an "Outdoor Cycle" workout. You are not expected to swing your arms when riding a bike.

Or maybe an "Indoor Walk", as that might accept you are using a treadmill, and your hands on the handholds (just a guess on this one).

Suggest sending feedback to Apple, as there are a lot of parents that jog with a baby-carriage.

https://www.apple.com/feedback/watch.html

The main way the watch count's your steps is by how (and how many times) you swing your watch wrist. Holding onto something while walking (especially on a treadmill) will not give you full credit toward your goals. I find the same "problem" when mowing the lawn. I don't know of any "fix" for this.