Ahh thank you for asking! I love this question and have a lot of thoughts on this. I'll start with the Tuckers!
-I don't think Thomas is Craig's biological dad. I think his bio dad is part Peruvian (to explain the black hair and I do love Peruvian Craig). Laura had a whirlwind romance with him and left her home in Colorado to be with him and got pregnant with Craig when she was pretty young. They broke up shortly after Craig was born and she returned home to Colorado with baby Craig in tow. That's where she met Thomas. I think they're both from around South Park, but I hc that Thomas is several years older than Laura. I think he was a sturdy, safe place for Laura to land. They got married when Craig was still very little, so Thomas is really the only father Craig has ever known and has always seen Thomas as "dad". When Thomas married Laura he also adopted Craig so that's why he's a Tucker! Then a few years later, Tricia came along.
-I think Thomas comes from a pretty conservative family and still holds a lot of those views (there's also some canon evidence of this too). I think he does have a hard time at first accepting that Craig is gay, but like in the show I think his love for Craig overshadows all of his doubts and although he struggles at times, he really does love Craig and comes to accept him as he is.
-I believe in Uncle Skeeter and Cousin Red! To explain Red's 'McArthur' last name, I kind of just assume her mom and Skeeter weren't married when she was born and maybe her mom gave her her last name? And her mom is remarried and Skeeter's an ol bachelor with a bar. I just love the idea of them being family. Tucker family get-togethers are just fun to think about!
-I think Craig and Grandma Tucker have a close relationship and she is one of his favorite people in the world even though she's Thomas's mom and not his bio grandmother, but she's always been Grandma to him!

Now for the Tweaks!
-Although I understand the canon evidence for it, I don't think the Tweaks are necessarily cruel parents. I hc them as extremely strict on Tweek with a lot of expectations that he just can't live up to. I think they can be quite critical of him. I think they can be distant and too focused on their work and don't always 'get' Tweek, but I do think they love him.
-I think the Tweaks are pretty well-off financially, particularly more than the Tuckers. I hc that the coffee shop does well but also that Helen comes from a wealthy family.
-Kind of related to that, I think Tweek has so many toys and gets pretty much anything he asks for. I think it's his parents way of trying to "make up" for not always being there for him.
-I think Tweek gets very mouthy with his parents and can be a total brat. It's probably a manifestation of his frustration with them.
-Idk how I feel about the "meth coffee" thing. I tend to hc that that is a rumor around town that was started because the Tweaks and Tweek are just so weird, but not actually true.

This was a lot of fun to answer! I'm sure I'll think of more and might have to revisit this one!