I imagine they got married after The Duke won over the approval of Toph’s parents. Toph felt that it was unnecessary, but because The Duke knew that Toph’s parents had been severely disappointed by her in the past, The Duke wanted to do his best to make her parents proud. 

Which other blog..?
If you’re referring to this post, it was an April fools’ joke :)

oh absolutely 

and Pipsqueak is actually very emotionally sensitive

he was very excited for the wedding

Basically, to be respectful to The Doph, Tokka, AND Sukka shippers, I’m going to address this in all practicality using logic and fair reason. So, here are the three possibilities regarding who the father of Lin Beifong is, answered in relation to Sokka.

1. Sokka has no relation to Lin whatsoever, other than possible “Uncle” (the endearing close-family-friend term, not the genetic term) or God-Father (or Spirit-Father or however they do things in the Avatar-verse). This is the most likely option, since I feel like Mike and Bryan have so heavily invested in Sukka over the course of three seasons in Avatar: The Last Airbender, that they would absolutely reject the idea of tearing them apart in a single episode of Legend of Korra for the sake of explaining who Lin’s father is. In this scenario we would assume - or at least, hope - that The Duke is Lin’s father.
2. Sokka is Lin’s step-father, and The Duke - or someone else - is Lin’s biological father. This can be used as appeal to both The Doph and Tokka shippers in that they were both together during certain periods of time, but this isn’t about appealing to shippers, it’s about practicality and explanations in the story. The idea would probably be that Toph and Sokka lost their respective spouses, and Sokka spent a lot of time with Toph to help her raise Lin since Toph worked arduous hours, leading to the two of them falling for each other and getting together. Technically, Sokka still isn’t Lin’s father, but it at least explains who raised her. 
3. Sokka is Lin’s father, and Mike and Bryan are going to challenge the media by implementing an incestual relationship into a cartoon on a children’s network. Considering that Mike and Bryan made the finale about suicide and existential crises, I feel like this challenge MAY be made by them, but I consider it extremely unlikely. 

In my honest opinion, based on practicality, analysis, and preference as well, I feel that Possibility 1 is going to end up being the answer. Whether The Duke is or isn’t Lin’s father, I’m fairly certain that Sokka won’t be. Because of the heavy story arc and investment behind Sukka, and because of the unlikeliness that Mike and Bryan would try to get incest past Nickelodeon, I strongly back Possibility 1.