whosegotmyeyebrows - no I'm not an idiot - but thanks for asking
I mangaged to disagree with your POV without calling you an idiot - even though I think it's idiotic to make statements like 'It's impossible to keep a child dressed while potty training'.
Yes, I have potty trained children and yes, they kept their clothes on when told to.
Do nurseries allow all the potty training children to run around naked? No.
Of course being naked in your own home is different to being naked at the shopping centre - my point is that the child should be doing as it's told not as it pleases. If you are able to make them keep their clothes on at a shopping centre, you are able to make them keep them on at home when you want to.
I'm a prude? LOL Yes, of course I am. I'm not even going to tell you in what way that is so laughable 
Really - you are being very dense. It is the Grandad that is bothered by the willy, not me. Why are you finding that so difficult to understand?
The OP wants Grandad to visit, Grandad is (for whatever reason) uncomfortable with her DS being naked (nope, don't understand it myself, but I accept it) so she has a choice - she either tells her DS to keep his pants on or she accepts Grandad wont visit.
You both let the children dictate what happens when you say 'you can't make them keep their clothes on', of course you can - you are the adult.
You don't have to be a control freak to bring children up to understand that when you say 'No' you mean 'No'.