I have a small crack theory on why Rin is so "weak" (Still beats the shit out of most demons) despite being the direct child of Satan and that's because there's still another seal on the sword. Firstly, Rin's demon form isn't like others, his demon trait stay relatively the same where as someone like Amaimon grows horns, has massive growth to his arms and gains a lizard tail. I think the flames fill in as where things should be, like his horns or tail. Secondly, Satan stated that he was going to break the sword to free his true power, of course this could be different now, most small details change like that. Now thirdly, Lightning's taken a real good interest into his sword, wanting to "tamper" with it, I wouldn't be surprised if he wanted to mess with the way his Heart was sealed and linking to this, Bon's father said if he had any problems with the sword to bring it to him, which could maybe be leading up to a future event where his Heart is unleashed fully.
As for why Mephisto put a secondary seal, I think he was scared of Rin getting too strong too quickly, he might've been a loose cannon and he needed to show the order he could be controlled to let him live. After all, you can't have a pawn that's stronger than you