Okay- I'll do my best with this. We use Sonlight. We started with Core 3 when dd (an advanced reader and very easy to teach) was in the middle of 4th grade. We bought the basic core- which is all they had then. We also bought their language arts and science, and used Saxon for math. You have to retrain yourself to not equate the core number with the grade. This was hard for me. I just started talking about them by historical subject- example- US history 1 for core 3, US history 2 for core 4, etc. That helped me a lot.
Yes, for that spread of years, you'd use two cores. You might be able to use two that went together: for example 1 and 6 (though that might require supplementing 6 for your 14 year old) because both are World History 1. Or if they still have the world history in one year at both levels- I think it was called core 1/2 or Alt 1 and for the older kids alt 6. Or you could do what we do and choose two cores that you think are best for your kids, whether the subjects are in sync or not. That's what I do. Dd was finishing up US history (core 4) when I started ds on core 1. She did World Cultures (core 5 and a great core, IMHO) this year, while he finished up world history with core 2. This year, ds is taking a year off because he's a late reader, his writing is horrible, and he's not ready for the amount of work (especially writing) in core 3- even at the regular reader level. We're doing Alpha Omega third grade instead.
There's a lot of reading in Sonlight- including parents reading aloud to the kids. No dd didn't like me to read to her, even the more complicated books, so I don't anymore. The first year (core 3) we read Johnny Tremaine out loud together, and Walk the World's Rim. She had no trouble with any of the books, but she was reading The Hobbit in first grade. Ds is the opposite, and I read a lot more aloud to him, which is what you're supposed to do even across history and science at the K-2 core levels.
I personally would pick a core based on where my children were in reading and history. I don't know about the 14 year old. I'm not crazy about the high school level choices Sonlight offers. History of the 20th century has some very heavy books, history of the Church looked interesting, but I don't know how helpful that would be in meeting requirements, and the social science doesn't cover some of the topics I'd like to see addressed. The 7 year old- if he's a very good reader and likes to write, core 3 would be all right. There's a big leap in expectations between 2 and 3.
I have no idea what the ultra cores, etc are. When we started they didn't have those. I chose a core, got the LA to go with it. Dd was always one level up in science - so we did core 3, LA 3, Sci. 5. I then picked a math curriculum. Last year I bought some of the art programs, but we rarely used them because my kids don't like to do art. We do music on our own.
Sorry for the rambling reply and extra advice you didn't ask for. I'm sure I just confused you more. I tend to do that.
I'm sure someone more concise can really help you out.
Julie