The other dog remains on her lead all the time, she's a beagle so she's owned by her nose and therefore we have no control if she was to get off her lead and run from us. When on walks, they are both on leads and the only house they ever visit is my mum's, simply because in two years we'll be living there anyway.
We have a beagle too, and she definitely stays on the lead at all times. We also have a lab, who we will let off the lead at a park, if there is no-one else at all around; but as soon as we see anyone approaching (even if they don't look to be coming to the actual park) she goes straight back on the lead. But our lab is very well trained and won't stray or even go too far from our beagle. We have a park just across the road from us (no play equipment, just open grass area with fence) which isn't specifically designated as a dog area, but where all the locals take their dogs to let them off the leashes to play games like frisbie, etc; there are quite a few other 'kids' parks (with equipment) in the area too, so there has never been a problem with this unoffical set up - it works for the community.

There is also a horse riding school down the road, so we often get many riders up around our neighbourhood.

The problem is, it doesn't really matter what is 'appropriate' or not, there will always be those people (pet owners) out there who ruin things for everyone. I love animals, my children love animals, but we try to teach them a health respect for them. This can be very hard when some dog owners will bring their pets right up to the children and let them jump and slobber all over them. We teach our kids that you never touch another dog (other then our own). If it is a little puppy or something, they have to first ask permission from myself or DH and then ask the pets owner if it is alright to give it a gentle pet. Often the answer is 'yes' (and then my kids know how to approach the animal properly and safely, and either DH and myself are right there with them) or sometimes the answer is 'no'; and my kids accept that too, because some animals just do not have the temprament for young children - and if the owner says 'no' their is likely a very good reason. I HATE it when other pet owners try to allow their animal to touch my kids without asking permission from me if it is all right for them to touch the dog, or tell me "it's alright" when I stop my kids approaching their animal. It is not alright. Unless you know an animal initmately yourself, it is always better to be wary around young kids (and sometimes even if you know them well things can still happen).