Just to echo the awkward situation sentiment.
Sounds like there are a few factors, and it may very well have absolutely nothing to do with the park or Cuddles's hair. Obviously you're not happy about missing the park, and I'm sure Cuddles feels the same way. You know, sometimes when we get a particular idea about something, it can be hard to change our minds - and perhaps that's what's happened with your parents and the park grass causing the allergy.
In your shoes, I'd sit down with the parents and just have a discussion - "We need to get to the bottom of this skin allergy problem so that Mum isn't constantly uncomfortable." Then make a list of all the things you think could possibly be the cause of the irritation - park grass goes at the top of the list. Each thing on the list will be eliminated from your mother's environment for seven days. If she is still experiencing the irritation during and at the end of the seven days, that thing returns to the environment and you move on to the next thing. So, if after a week away from the park, your mother is still scratching, you and Cuddles are allowed to return to the park because it's been ruled out as a contributing factor. When you are eliminating Cuddles's hair from the environment, keep up the good work you've been doing with the grooming and vacuum frequently. However, I have to say I would think it strange for your mother to suddenly develop a contact allergy to an animal she's previously had no problems with. I developed hayfever after I got my shepherd, but unlike your dog, my shepherd sheds like a demon - I could make another dog from the hair that comes off her in a month. I get congested when I haven't vacuumed for a few days, but I don't have skin problems. Of course, the fact that it hasn't happened to me doesn't mean that it couldn't happen to your mother or anyone else, but just to cite an example, I guess.
When your mum had the allergy testing, do you know whether a particular type of grass was flagged? Just putting that out there because there are so many different types of grass. I mean, my kelpie is allergic to (amongst other things) paspalum grass, but she's absolutely fine with the regular buffalo and carpet that comprise my lawn. Is there grass in your backyard? What is it about this particular grass in the park that your parents feel is causing the allergy more than anything else?
Like you said as well, it seems strange that she's developed this symptom only after the surgery. Is it possible to find out whether her new medication could be contributing to the issue - not necessarily that she's allergic to it, but, say, it may cause skin sensitivity in some patients? Does your mum have a rash or visible sign of irritation, or is it just that she feels itchy? Just wondering how you might be able to narrow down the list of suspects, so that you can find a solution to the problem for both your mother and Cuddles's sakes.
