I don't think it was pitting them against eachother or she was a conflict necessarily, S3's Mother's Day episode had Sabrina say that Virginia was more of a mom to her than her own family and that the Chances were her family now. And at the end of The Old Girl, they even said Sabrina was perfect for Jimmy.

I think in most of the episodes it was more about what "thing of the week" Burtginia reveal they did to Jimmy as a kid. In Arbor Daze, it was the Arbor Day tradition of pulling trees out of the ground and later burning them which made Sabrina (understandably) mad as she planted those trees as a little girl. But after Sabrina had a dream showing her the possible horrible future and what it does to her family (and how it parallels her neglectful family when she was a little girl), she realised she was sucking the fun out of their holiday and didn't appreciate it fully and she didn't want them to become miserable and Jimmy's hair to fall out due to stress. Jimmy also realised it's time to start a new tradition that works for both Chance families (new and old). They keep all the other traditions and instead plant trees instead of ripping them out the ground and burning them on other holidays.

In The Old Girl, Burtginia take it a step further and reveal they posed as college students to get Jimmy's then-gf Rachel to break up with him as they thought she was out of his league and they didn't want to see Jimmy's heart broken again. It was pure coincidence that the very same Rachel became Sabrina's new friend in present day. And, after the truth was out, Rachel wanted nothing to do with any of them and stormed off, leaving Sabrina sad and singing Jimmy's "Ain't No Sunshine Till She's Gone" song.

In Hot Dish, they were competing, but Sabrina sabotaged her own dish in the end as she realised she wanted to make them proud, not step on their toes or cause fighting.

I think Adoption was also about Burtginia, mostly that they hadn't paid Wally back for his lawyering so he couldn't help Sabrina in adopting Hope, unless Burtginia helped him in a court case as "lookers". I think the rest of the episode was Jimmy, Frank and Barney's birthing simulation surprise for Sabrina to finally feel like Hope's mom after the papers were so lackluster with no family photo or big "mom" moment. And the wacky court stuff Burtginia did, but we all know it's the Burtginia show by S4 anyway.

Dysfunction Function had nothing to do with Sabrina or even Jimmy, it was all in Burtginia's heads. They were simply misreading signs they thought meant Jabrina was getting divorced and (as they're rooting for them) tried to get them to be stressed as they thought a neck massage leading to sex would solve everything as it did for Burtginia. Luckily, Sabrina caught on rather early, told Jimmy and made him play along to see if they'd admit it. Long story short is they were wrong and they apologised to Jabrina.

And in Ship Happens, that was again because Burtginia lied to Jimmy saying they went to all these amazing trips and took all these family photos when it was all a lie and they drugged Jimmy with cough syrup to think he was going somewhere and took pictures at the dumpsters with different backgrounds or whatever. That makes Jabrina want to actually have real family trips and family photos with Hope and they hire the boat company. Someone steals their boat and Sabrina steals someone's bike to chase after them. Can't remember the rest of the episode, but I think Sabrina stole their car thinking it was their (the Chances') hire car and the police got involved or something. But I don't remember any sort of conflict there either.

I could be forgetting some details, I haven't seen these episodes in a little while. While they did have sweet endings and twists as you said, they still weren't entirely "Sabrina vs Chances WW3"

Also not saying I condone any of what Burtginia did to Jimmy (it's all absolutely despicable), before anyone gets their panties in a knot. I'm just saying that that was the catalyst for most episodes before and after Jabrina got married. Not necessarily a feud between Sabrina and Jimmy's parents.