I appreciate the image but I can't really tell what you are trying to do without a document to look at. What you're saying is synonymous with click a button pause the timeline, click another start a different timeline. Which as i explained you can accomplish with the different actions. It might be better to look at using functions where you can accomplish the same using Hype's API. This way you could tie the start and pause actions to the same button. Which I think in your case is what you want.
The logic being .... press CROWN and the associated timeline plays. Press DOOR & WINDOW and the crown timeline pauses and the door & window timeline plays. Hype has a built in method for telling you if a certain timeline is playing.
You could essentially check all timelines to see if they are playing or not. And then pause the ones which are and start the one you want.
A document would mean that we could tailor something for you. If I have time I'll try and post something that would demonstrate what I'm saying. Or someone else might beat me to it. But in any case a document would make things mush easier for you. There is probably more than one way to do what it is but at the moment it's like a stab in the dark.