The picture helps greatly. I can see why extensive fencing isn't feasible without an unreasonable cash outlay. Sucks that they are the problem but you have to bear the burden of work and expense to mitigate their irresponsible behaviors.
Unfortunately you will probably have to add more fencing and security at some point to reduce their incursions. Perhaps the rolled goat fencing along part of the border? Or a few more low strands of barbed wire.
Once decent weather arrives do you plan to extend grazing areas for the sheep and goats? It won't take them long to strip small areas and you will probably need to rotate pastures anyway for parasite control.
Pasture rotation will be used extensively in years to come, in part for parasite control. No more than 12 ewes plus age-0 offspring and 6 does plus age-0 offspring will be kept, in addition to alpacas. A donkey is being considered for running with alpacas. Alpacas are not to be pastured with the ruminants to avoid health issues for alpacas. The barnyard area represents only about 1/2 acre and will serve as winter quarters for my adult gamefowl free-range core area young of year during production season. Roughly 12 acres of additional ground will be used for grazing other animals. That additional ground will be broken up into about 12 paddocks where one paddock will support adult gamefowl during the production season. That paddock will be a good example of silvopasture.
Strip grazing may even be part of approach while I have age-o stock in finishing phase. They will be pasture finished rather than grain / hay in a dry lot.
Only the barnyard area will have the sheep and goat panels as they are far more expensive than other fencing options. The more cost-effective fencing for stock confinement will not be reliable for excluding roaming dogs and even my pack of 5 dogs plus a jenny will be hard pressed to defend all area from a pack like I'm dealing with now.
I want to expand land use for sheep and goats outside the barnyard area by spring once they consume vegetation down to point where I can topseed. The sheep and goats will be used to manage vegetation throughout property with some areas managed to support wildlife. That means the number of head per acre will be low, as in low enough we can go through winters with little or no need for hay except for when snow is heavy. Some of ewes and does will be used for dairy purposes and may need be moved a considerable distance each day.
My English Shepherds will have dual responsibility of keeping predators out and moving stock in the event I have trouble getting them to go somewhere by training. Only one dog at a time will be used for moving stock and it may not be used routinely for predator management. Integration of jenny and my dogs will be a challenge to address.
@ChickensComeHome2Roost I already keep honeybees with one apiary / beeyard in orchard currently used as winter quarters for adult gamefowl and another apiary south of barnyard area. Neither excludes animals or people.
This place is a training ground for children so is going to have a diversity of approaches and land use at any given time.