I never got a sense of the “bad parents” thing.
It’s not phrased like that in the movie, but the muscle in the First Order is Han and Leia’s son, who went to the dark side. And Han and Leia question themselves over why it happened.
And it’s also said by Solo that the reason the supreme ruler or whatever wants him is for his power.
I find it very over the top and not entirely serious to have a plot which hinges on the premise that Han and Leia could’ve done simply something, or many things differently with their son, but that now the whole galaxy is experiencing a total reboot of the same threat as in Episode IV.
It must be hard for those two to know that they’re responsible for the troubles now facing everyone - though the movie doesn’t acknowledge this. They had a son, and whoops, all the rebels victories are now undone and everything is right back to where they were.