Why the fence cat drives her to distraction
Whether or not the cat intends to tease, the effect on your dog is the same: a rival animal sits elevated, motionless and staring, right on the boundary of her territory, and stays there. Barking is her attempt to move it along, and because the cat eventually leaves on its own schedule, she learns that enough barking works, which guarantees a longer performance next time. The fence adds frustration, since she can see and hear the cat but cannot reach or properly investigate it, and frustration barking escalates quickly into a habit that generalises to any animal on the fence. Neighbours hear all of this, of course, which adds social pressure to fix it fast. The fix is to change what the cat's appearance predicts: not a barking shift, but a recall that pays.
Interrupt early, before the barking locks in
Timing decides whether your recall stands a chance. Call her the moment you see the ear-prick and hard stare, ideally as the cat first appears, and reward her generously for turning away from something that interesting. Once she is in full voice, hackles up and bouncing at the fence, her arousal is too high for learning; bring her indoors calmly on a lead if needed and try again next time at an earlier moment. Keep a long line on her in the garden during training if your recall is unreliable near the fence, so you can prevent a full rehearsal without grabbing at her. Every completed barking episode at the fence is practice for the habit, so management that cuts episodes short is training, not cheating.
Teach her the cat means look back at you
Practise deliberately when the cat is present but she is still calm, starting as far from the fence as your garden allows. Let her notice the cat, say her name or a watch cue, and reward the look back with something excellent, then move away together or start a game. Over sessions, let the distance shrink only as fast as her responses stay easy. You are building a new emotional association, cat appears and good things come from my person, which competes with the territorial script. Keep sessions brief and frequent rather than one long standoff, and end them by going inside while she is still succeeding, not after she has tipped into barking.
Lower the trigger while the training builds
A visual break along that stretch of fence, such as screening or planting, can reduce the cat's looming presence while her new habits form, though determined cats often simply choose a new perch. Learn the cat's routine if you can; many fence-sitters keep regular sunbathing hours, and scheduling her main garden play for other times removes daily rehearsals. A friendly word with the neighbour can help too, not to demand the cat be kept in, which is rarely reasonable, but so they understand you are training and may occasionally ask them to call their cat in during a practice session. If her reactivity extends to every passing animal, person and sound at the boundary, or she is injuring herself throwing at the fence, discuss the wider pattern with your veterinarian and consider a qualified behaviour professional.
Keep garden practice consistent across the household
She will learn fastest when everyone responds to the cat's arrival the same way: early recall, generous reward, indoors if the moment is lost, no one letting her bark it out because they are busy. Agree the plan and the cat's usual hours as a household so garden time gets supervised during the risky window. In KinsLe, Care Teams lets you set the fence-practice sessions and supervised garden times as shared duties with their completions noted, so whoever is home catches the cat's appearance at the same early moment you would.