Got me but if the town doesn't have zoning regs against manufactured homes on foundations, I don't know that someone selling a single parcel can do so. You could potentially challenge that clause is court if necessary. Easier if you can find cases where similar clauses have been found unenforcible and just show them to the guy. Tell him you aren't going to drag a 1960's rat trap over and live in it. There are some truly fancy "trailers" made these days. They may look like a standard mobile home on the outside simply due to the restrictions of roadway width but they don't have to look like "trailer trash lives here". Heck a "basic" stick built ranch home doesn't look any different than a double wide.
Covenants like that at are more usual if there is a neighborhood association that makes rules that apply to all. For instance, the 8 houses up the hill are on a private road. The land used to belong to the property we live on until the prior owners chunked it off. Their rules say "no poultry". I have no idea why. Near as I can tell they could have llamas (specified in fact), pigs, horses maybe even cattle but not poultry. They could, of course, change their association rules according to whatever method they have to do so.
With regard to the yappy dogs that aren't kept home, I would have reported the lady and the dog that bit you. They have been a longstanding problem for the neighborhood and don't deserve "one free pass". Her dogs are an annoyance to many and she knows it. That bite report will put the dog on a short list. The lady would be told that if the dog bites anyone else it will be destroyed (different places might have different "number of bites"). That might be enough that she will keep them on her own property. If you don't feel like shooting it with a "weapon" of any sort, capture it the next time it comes on your property and take it to the nearest shelter, no matter how far away that is. Since she knows she isn't properly keeping her dogs at home, I don't think I would even tell her you did so. Let her think her "precious" dog got run over somewhere. Let her sweat. If it has tags, they might call her to come get it. That can get pretty expensive, again she might be convinced to keep them at home. BTW, if you are concerned a BB gun would damage the dogs, I've not ever "played" paintball but I gather they can sting pretty good. Might do some serious damage to a 3 pound rat at close distance. Maybe a "super soaker" instead? And given her lack of desire to control her dogs at all, were I walking down the road and her dog(s) came on the attack (even if they stop short) I would likely give them the same treatment
@CntryBoy777 suggested, try to land them on her doorstep

Not quite the same as a dog that gets out one time and harasses people.
The kids across the street?? Wow. I would call the law on them. Trespassing on your property. Shooting toward your house? Better the law comes down on them before someone gets hurt.