to go and check what DS1 is up to at the park?

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He's 10 and just recently been allowed to go and meet up with local friends at the nearby playing fields/rec.

He's been gone and hour and I've told him to be home by 7pm.

When DH gets home shortly, I'm going out for a run (DH will need to stay with DS2). Would it be unreasonable of me to "happen" to run through the park and see what they're up to?

yanbu, I would do the same (and am quite a slacker mum in most respects)

No - it would not be unreasonable at all :)

Whether he agrees though is quite another thing! Mind you, if he gets stroppy I'd be telling him to sort himself out as the park is a public park and that's where you run! It will keep them all on their toes too - being allowed out doesn't mean being able to do as you please