Sistine Chapel

Nope. The chapel is at the furthest end of the museums; you have to pass through parts of them to get to it. Without stopping to look at anything, the usual estimate is a brisk 1/2 hour walk from entrance to chapel but that time could be affected by the density of the mob that's in front of you.

The Gallery of Maps is a section you have to pass through, and it can look like this:
https://www.glencanning.com/2024/10/31/the-crowds-of-rome/

If by "tour" you meant a guided tour that does only the Sistine and no other part of the museums, I'm not aware of one, and it would have to use the route everyone else does anyway.

Kathy, your attachment pictures capture the crowds that we experienced at the Vatican, and that was in spring, 2017. I can't imagine the museums even more crowded. And- that's the crowding that we experienced throughout the three hours (I think) tour. It's difficult to imagine.
Thanks for adding, as a picture says so much.
Safe travels!

I think you could probably get from the entrance to the Sistine Chapel in 15 minutes or so if you walk fast, study the map for less-crowded routes and aggressively shove through crowds when you encounter them. We took a tour through the museum and there seemed to be a standard route that everyone followed, so finding an alternative could speed things up. You could also book the first entry time in the morning and then run ahead of everyone else.

Of course, there’s also the question of why one would want to rush so hard, shove past everyone and ignore everything else in the museum.

I’m asking for sister and brother in law who have mobility issues

Kathy, wow, that picture is insane. I’m so glad I visited those sites when I was in Rome in 1999. It definitely DID NOT have crowds like that. And to answer the OP’s question, tickets are together. What kind of mobility issues? Canes? Crutches? Wheelchair? All can be utilized there. I’d contact them directly, either by phone or email to ask, because anecdote does not equal data.

And to answer the OP’s question, tickets are together.

I'm thinking that you mean that the chapel isn't a separate attraction; Correct, it's part of the museums so it's all on a single ticket.
The Museums website has information regarding visiting with mobility challenges, and it mostly concerns wheelchairs. There's an accessible route for those, and it's possible your relatives can use it to get to the Sistine but it still involves passing through sections of the museums.

https://www.museivaticani.va/content/museivaticani/en/organizza-visita/servizi-per-i-visitatori/accessibilita.html
https://www.museivaticani.va/content/dam/museivaticani/pdf/visita_musei/servizi_visitatori/mappa_disabili_en.pdf

If the museum still does night openings, the crowds might be lighter then.

Kathy's picture is exactly what we experienced last year. It was insane. Although we had been to the Vatican before, we traveled with a friend who had never been, so we opted to do another visit. Instead of doing the museums, etc. we opted for the Vatican Gardens tour that included the Sistine Chapel. We loved the gardens, and we had a small group. The Vatican guide was excellent, BUT, we did have to endure the hoards as depicted in the photo link above (Gallery of Maps hallway) and the stairs down to the Sistine Chapel. It was again, insane. We felt like we were breathing everyone else's expelled air. If you are skittish, I suggest wearing a mask. For the long walk and wait, they pretty much herd you along once you enter. Is the Sistine Chapel worth it? Definitely. Just be prepared for crowds.

Depending on how much lead time you have, you could also try and book the first entry time in the morning and get to the museum extra early so you’re in the front of the line. Then most of the crowd would be behind you as you proceed through the museum.