You could try to go to the Police Department when she is working and ask to speak to her. Be polite and state your case, and tell her your just trying to resolve it without a hassle.
I favor this approach. Clearly catching them at home isn't working. But I wouldn't attempt to have the conversation at her workplace, because no one likes to have their private life intrude on their work. Showing up at her work place WILL let her know that you are serious in your complaint though - I'd approach her at work and ask her to stop by your house when she finishes her shift, if possible, for coffee and a conversation. Emphasize that you'd REALLY like to speak to her, and soon, if she tries to say she's got something else to do.
Here's my thought on the subject - they probably don't realize how FREQUENTLY he's doing it, and I'm SURE they don't realize the inconvenience and misery it's causing you - because they don't take their dog out to potty on a leash they won't be considering the fact that you DO, nor what that involves. So they are probably thinking that you're just complaining about poop in your yard, which since they are clearly not responsible dog owners no doubt doesn't seem like a big deal to them. I'm betting they've complained to one another about it in the house, "oh our neighbor is being such a b****. What's the big deal?" Not the case, of course, but the first obstacle you have to overcome before things can become constructive between you folks will be their hostility/wish to totally reject your complaint as "whining."
So first things first: establish empathy. Once you've got your captive audience, explain to her that you walk your dog early in the morning in your yard, when it's freakin' cold, and she won't go because this strange dog is invading her territory and the smells are all wrong, and it's making you late for work and causing you to have to stand out in the cold for long periods of time, and in general it's making your mornings miserable. I'd explain the areas that the dog is invading through, and how it's impossible for you to close off your driveways although you DID fix the break in YOUR hedge fence.
I'd remind her about the leash laws in your town, and whatever regulations cover this situation, and the possible consequences - (but couch this gently).
And then to keep the peace I'd throw out some phrases like, "don't want to ruin our good relationship" and "just want to be good neighbors and hope we can work something out" and "didn't really want to involve the dog warden...yet" and "very sorry that this is becoming such an issue for all of us." And then ask her if she's got any thoughts about how the issue can be resolved. Offer up advice/cost analysis about invisible fences and above-ground fences, boundary training techniques etc just to show that you're being constructive about the issue, but make it clear that the issue is HERS to resolve because it is her dog that is wandering onto your property. You might also mention that the testicles are a big portion of why he's roaming, and looking for love in all the wrong places.
