I agree no dogs in playground. You can't always control where your dog needs to answer a call of nature and kids shouldn't have to be worried about watching for 'accidents' in their playground.
However, I have a dog. I struggled with the dog at first as he was very 'naughty' for want of a better word, I was pregnant (found out just after we got dog) and then had a baby plus 2 older kids. So dog went to dog sitter on days when my husband was at work. However, now he's calmed down a great deal and I can cope with him and am saving money by not using the sitter. But he needs to be walked obviously. During the day I often go to a baby group so once I've done that I want a bit of time to relax, feed the baby etc at home before school pick up time. So for me the best times to walk the dog are when I take the kids to school and when I collect the kids from school. We live a 25 minute walk away plus there's a park we can detour through on our way back so it gives the dog a really good couple of walks.
But school has specifically asked parents, by letter, not to bring their dogs to school. Not just into the playground but anywhere near the school. The path outside the school is always littered with dog poo but none of it has ever been from my dog and I don't think it's even dogs of families at the school, just people walking their dogs past on a night.
So last week I took the dog and stood on the pavement opposite the school gate. Once the crowds had cleared a bit I could see my kids waiting and when I waved they saw me and came. Which would have been fine except a teacher insisted on accompanying them across the playground and out of the gate. She tried to cross them over but I called over than I'd meet them at the lollipop man further down. I felt a bit guilty that she'd had to leave her post at the door and come over with my children but really, why did she have to? They're not 4, they're 9 and 10 and had clearly seen me, as had staff. But anyway, I'm not sure whether school see it as acceptable for me to bring the dog to pick up but, like I said, it's the best time of day for me to walk him.