There are some dogs that are in our area that were seriously traumatized by events in the past. Sadly, many of them never get over this no matter how much you try to change their minds. One that comes to mind in particular is a 4 year old mixed breed that was abused by children as a pup. Even though she has been carefully looked after and perhaps pampered since then, she cannot be allowed around children and will bite them if they get close. We have to identify these afflictions in dogs when finding them a forever home because obviously bringing this particular dog to a house with a child could and likely would result in disaster. She does not react this way to anyone that is over a meter tall or so.
While I am not completely familiar with the rules that Muslims have towards dogs I believe you are correct. There is another one that I heard about where they cannot touch a dog that is wet, or something along those lines.
Sounds terrible because most dogs are good with kids and explains everything the abuse she must have endured. Muslims bend their own rules to suit themselves and I am sure there is a list when it comes to animals. One neighbor once asked us to slaughter his goat and we had no idea he had a goat, but they have to get it blessed etc and we refused to do his dirty work.
I would say that is a very bizarre request to ask your neighbor to slaughter a goat for you.