Walking burns calories because it is weight bearing exercise - you have to lift your bodyweight (even if just a fraction of an inch) with every step. But with a stroller, the extra weight goes down through the wheels, not through your legs. With a good stroller on level ground, the additional calorie burn is minimal.
Certainly on hills, you will burn slightly more than just by walking yourself. An HRM is probably the most straightforward way of estimating this, but if it is beyond your budget, it is beyond your budget.
If you want to account for the hills, perhaps use a website like mapmywalk.com which will allow you to estimate the vertical gain during your walk. One vertical foot is roughly equivalent in effort to eight horizonal feet, so add this to the total distance travelled.
In terms of the stroller on hills, the additional calorie burn is probably less than 5%.
The reasonable man adapts himself to the world; the unreasonable one persists in trying to adapt the world to himself. Therefore all progress depends on the unreasonable man.
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