The New-Runs were created so the author could avoid bashing Anthony.
With the supposedly happy marriage of Elizabeth and Anthony, Johnston inadvertently wrote herself into a corner. While men are generally depicted as boorish and neglectful of their wives — even fragile genius Mike — having Anthony turn out to be just the same would've damaged the whole "man of destiny" vibe she was going for. Plus, she wanted a way to keep working out her anger towards her ex-husband. When she couldn't figure out a way to portray a geniunely happy union between them, she fell back on what she knew. This way, she can Ret Con John Patterson into an even bigger Jerk Ass and avoid tarnishing her precious Anthony.
Everything after April falls into the stream is a Fix Fic written by Michael to cope with losing his baby sister.
Farley's Heroic Sacrifice and Edgar's Timmy In A Well - and everyone rushing to the rescue - never happened. By the time they realized April was missing, it was too late. The loss hit the Pattersons hard; on the suggestion of a friend, Micheal tried writing about it. Unable to cope directly with his feelings, he speculated instead on what might have been, if only things had worked out a little differently. This eventually ballooned into the Wish Fulfillment seen in the published strip; after all, why not make things perfect in his fantasy version?
* April is heavily idealized, yet her parents treat her as The Un Favorite because Michael can't picture them actually treating one of their children well, thanks to his own shoddy childhood. The best he can come up with is having them ignore her.
* Similarly, he doesn't recognize that the way he treats his "ideal family" is less than ideal because that's what he grew up with. He's merely taking what he learned to its natural conclusion. Deanna doesn't protest because she's nothing more than a fantasy of the "perfect wife". The kids are bratty for the sake of being bratty because that's what Elly always claimed he and his sisters were.
* His own Purity Sueness is how he'd like his life to have gone; even the setbacks all "pay off" for him in the long run.
Anthony was going to have Therese murdered.
He pleaded for Elizabeth to "wait for him", yet Therese was vilified further for daring to divorce him. But if he wasn't planning to divorce Therese anyway so he could get together with Liz, he must have had some other plan in mind for getting rid of his unwanted wife... Thus, Murder Is The Best Solution. Therese was always going to work instead of staying home like she should have been; therefore, an oh-so-tragically-random mugging in the parking lot and her brutal murder would only be her just reward for daring to have goals and dreams outside her assigned gender role. Plus, this would mean they'd get the insurance money, and he'd come off as an even more tragic character, the poor pitiful widower left raising his baby girl all by his lonesome self... until Liz got her act together and threw herself into his waiting arms.
Fortunately for Therese, since Good People sit around and wait for opporunties to be handed to them on a silver platter, Anthony was still patiently waiting for a suitably hardened criminal to drop into his lap before making the arrangements. As a result, eviiiil Therese beat him to the punch by hitting him with divorce papers and taking off on her own, having the sheer nerve to stay alive instead of dying for her 'sins'. The cheek of that woman—!
* Alternately, he wasn't even going to make any arrangements; he just assumed she'd get what was coming to her soon enough and he wouldn't have to lift a finger. The fact that she divorced him instead of getting herself killed still shocked him, because he'd assumed she'd stay with him despite his not making any effort to help their marriage work, just because that's the way he thought the world worked.
Elly and John approved of Anthony because he reminded them of Elly more than John.
By his own admission (though he didn't actually recognize it as such), Anthony is extremely passive-aggressive and tries to manipulate others without really understanding how they tick. He has a very narrow, conservative mindview and doesn't know how to deal with any alternate points of view. Therese's reluctance to start a family stymied him because Female Success Is Family, isn't it...? Thus he blatantly lied to her, expecting that her female instincts would override all her stated plans and wishes once their child was born. When Francoise was born, he was stunned when Therese did precisely what she said she'd do and expected him to keep his promise... and made her out as the villain because she wasn't doing exactly what he wanted without being told.
While both of the Patterson parents have this problem, it's far more prevalent in Elly than it is in John — and more importantly, because the strip focuses on her, the audience is meant to feel sorry for her while deriding John for the same flaws. Elly is a poor, put-upon housewife because she doesn't understand John or the kids; meanwhile, John and the kids are horrible because they don't understand her. If we were meant to see Anthony as being similar to John, then he'd be unsympathetic; since we're meant to praise him, the parallel with Elly is stronger.
Elly actually manages to pick up on this, making Anthony a rarity — a guy that she understands. That makes him perfect for her daughter, because she can actually comprehend somewhat why he acts the way he does. (This is also the cause of John's disturbing No Yay vibe with Anthony; of course they seem to connect — he's just like his wife! Only male and not a strange, strange female!)
* Consider also: in Real Life, Lynn was divorced and had a son when she met her second husband, who became the basis for John Patterson. She's also stated that the courtship of Liz and Anthony was based on their relationship... so Anthony could very well have become another stand-in for Lynn, just Gender Flipped! Anthony maps to Lynn, Therese becomes her demonized ex, Francoise is her young child, and Liz becomes her "ideal mate" — someone who (unlike her second ex-husband) is willing to give up everything in a heartbeat just for the privilege of being with 'her'.
April became The Unfavorite after falling in the river.
A four-year-old nearly drowning and being saved by a Heroic Dog's final act would be pretty big news and would make the rounds in Milborough, meaning that everyone would be talking about it... and, quite frankly, passing snap judgements based on whatever information they got. They'd likely ask unpleasant questions like "What was a four-year-old doing unsupervised anyway?" or "How'd she get out of the yard without anyone noticing?" Elly is very self-absorbed and extremely conscious of others' opinions; even if nobody ever said anything to her, the mere thought of others silently judging her the same way she judges everyone else would leave her terrified — and outraged.
And who's to blame for the accident? Certainly not herself — no, it must be that ungrateful, horrible brat April! She never forgave April for that horrible embarrassment, viewing her from that point on as the troublemaking little snot that damaged her reputation.
* April, for her part, picked up on this at an early age, though she didn't understand why her mom disliked her. She acted like a Deliberately Cute Child for years after she should have grown out of that stage out of a need to please her mother, thinking that she preferred cutesy childish antics to a kid's regular behavior. However, she eventually realized she could never please Elly decided to focus on doing what she liked instead, not trying to gain her mother's favor. Ironically, in making this realization, she managed to "out-mature" her older siblings, and ultimately escaped her parents' meddling influence.
Since, to my knowledge, nobody in THIS community has accused Anthony of plotting Therese's murder, we can say that they hate him just a touch more than we do.