Here’s a more specific suggestion. I have several favorite authors, and like you, I prefer not to read a story focused on explicit sex. Three of my favorite authors are Geron Kees, Mikiesboy, and lomax61. Geron does tend to include science fiction characteristics in many of his stories, but if you don’t usually like sci-fi, sample the first chapters before you skip the story (you might find that you like his storytelling enough to get hooked – I did with his take on Zombies). Tim (aka Mikiesboy) has written an extremely wide variety of stories with all sorts of situations and characters. Brian (aka lomax61) creates unusual situations with interesting characters who sometimes cameo in his later series (Hooking Trout was controversial and the unhappy reactions to the story mean that it will probably never be completed).
Checking your Profile tells me you’re a few years older than I am.
Tim wrote Changes about a married couple.
northie has two sets of characters who are ‘more established’ than many of the protagonists on GA. Soul Music and Never Too Late will both be going on a hiatus until next year, but each has plenty of chapters to keep you busy. Never Too Late features a curmudgeonly, but lovable character who is retired and slowly Coming Out. northie is English and these two series are set in England.
Geron’s Doorways series does feature a grandfather (less so in the first story in the series).
I hope this helps!
;–)