I don't see Odium about severing connections, that is thinking too black and white.
I see Odium more about retaliation, but with internal emotion built into it. Odium didn't like that Elantris spoils
, Honor and Cultivation broke a supposed pact(which I believe was they agreed that they would not put the shards back together, which being on the same world isn't really doing that, but it is why some could see it as so). But this gives reason/strength for Odium to go after them, it allows the shard and Rayse to try to splinter them. I believe this is why he could easily splinter D&D and Honor and why splintering Ambition was much harder, Odium's intent didn't match to splinter Ambition like it did the others. It was something that Rayse wanted, not the shard.
On the Honor part, even Honor(I am guessing Tanavast in this case) didn't even teach the spren to do so. So you are somewhat right on that count.