Yes, it is possible that Sona’s dad knows where the kid is and engineers the whole thing.
I get why Luthras were mad at Sona. Giving her the benefit of doubt that she couldn’t reach Karan or was too young to handle her pregnancy, she very well knew where the Luthras lived so she could have reached out to the elders as they knew her quite well too. Things would have been lot different if she had confided in her dad and he could have reached out to the Luthra family.
Even if she couldn’t do all of the above, she could have just stayed away and not come back in Karan’s life pretending nothing happened in the past. Then when confronted she lied and then accepted. Whole lot of unnecessary drama/trauma for her and them.