Regarding shoves, there actually does appear to be a resistance check, presumably with the DC being the shover's athletics versus the shovee's athletics or acrobatics, whichever is higher. Bugbears are pretty strong so they're not bad at shoving. That said, it really does sound to me as if you're not positioning a whole lot before that fight and you're giving the grunt a good angle. Also possibly without really doing much to avoid being in LoS from below. I have not really checked out the gobbo hole mechanics much, but do notice the raised plateau right next to those bugbears. That's probably where you want your party members, if hugging the weakened wall isn't doing it. I would very strongly recommend ungrouping your party (there is a button for this now, but it is unassigned by default) and finding good positions for them individually.
A 10 meter shove does sound rather ridiculous, though. Would your fighter be a dex-based hafling or gnome or such? And I'm assuming without proficiency in acrobatics? Otherwise it sounds like a bug more than anything. I have not seen normal sized characters get pushed that far by other normal sized characters, but I am fairly sure that shove distance is affected by shover strength and size versus target's weight and maybe size. Which makes sense, you have to admit, even though 10 meter shoves from unexceptional enemies is of curse quite ridiculous.
Edit: I just noticed your other topic on that shove, and it seems like you fell down a pit? That does change things. Obviously that's not how a drop works in real life, but the game seems to maintain your horizontal movement speed during descent, so the further you fall down, the further you move horizontally. And moving 10 meters that way is very possible, even though it is obviously nonsense.
About the shove resistance check, I looked carefully everytime, and there wasn't a Save dice icon appearing.
My fighter is a 16 STR human with proficiency in Athletics.
I attempted that encounter 5 times, and even when I was hugging the wall behind the sleeping bugbears, they could find a way to shove me down the ledge.
I calculated the distance from my character to the ledge, not including the falling distance.
