I wouldn't go so far as to call him a horrible father. He did poorly in his response to Amnon's raping of his half sister, and we can only speculate why, (after all what he had done was rather shameful to start with) but he did a great job with Solomon. Now Solomon clearly went overboard on the number of wives he had, but his children did not have any drama or acting out, or murder or whatever but then again, Nathan clearly told David the reason that he was about to experience the heartache and bloodshed that ensued. We can look at what Absalom did as poor parenting, or as backlash for the failure to respond to what Amnon did. Two other sons are mentioned, one of whom tried to usurp the throne and if he had not asked for Abishag to be his wife, Solomon would not have put him to death, but then again, blaming that on poor parenting, would be ignoring the judgment that Nathan pronounced, and the specific reason why that was announced, was that he (David) had taken Bathsheba to be his wife and had her husband killed by the Ammonites. One other son of David is mentioned, and he was Chileab, born to Abigail, and we never hear of anything good or bad about him, as he seems to have slipped off into relative obscurity.
I think we look at single mothers today, and see how many children raised in that environment, turn out to be poor adults in society, and extrapolate that to what we think would happen in a polygamous family where the man has too many wives. When we look at how large families actually turn out, Josh Duggat notwithstanding, and even he isn't as bad as a lot of those raised by single mothers, well, we can take a look at the Bountiful, and the guy has like 11 wives, and his children are quite industrious. We can look at Philip Sharp. These men do have flaws, but have managed to raise decent hard working children.