I don't think Yutarama would be the grand mastermind, at least for malicious reasons. I'm certain she sent Ilulu to hunt Kobayashi after hearing what happened between her and the Emperor of Demise, and became more interested in Kobayashi after Iruru was dealt with.
There are many dragons who can use dimensional travel, after all Elma followed Tohru, I also think that Fafnir and Lucoa came through by their own means. Kanna was sent through because of her pranking, and possibly because she liked using her human form, who done it is pretty open, and there could be many candidates for it, hence why she has no idea.
I kinda understand why Coolkyou wants to make Yutarama a major player in the manga, after all Kobayashi is acquainted with Telne, the second highest in the harmony faction and Lucoa, one of the most powerful people in the other world, having a stated powerhouse of the chaos faction will balance it out.