There are two separate questions going on here (Vatican and Colosseum/Forum/Palatine) with two separate situations as traveling with the 79 year-old parent is a bit different than not.
Vatican: I saw the Sistine back in the early 70's in relative peace. Took the Husband there in 2007 and it was a madhouse. It's reported to be even worse now. Whether to take a tour or not depends on exactly what you want to see and how you want your information delivered. Some tourists feel the early-opening tours were worth the price to see the Sistine without the crush/waiting in a queue to get into the chapel, having a guide navigate some highlights throughout miles (yes, miles) of stuff in the museums, and to have their information delivered by a human. Guided tours also assure that you can take that shortcut into the basilica: access is not a given for independent visitors as it's up to the whim of the guards on any given day.
The Museums also offer late openings (Friday nights only) from April- October that are reported to be less of a crush and not as overly warm in the galleries during the summer season. Not all areas of the museums are open and there's no access to the Basilica but the usual highlights - including the Sistine - are accessible. You can do it either DIY or with the tour. Available for bookings on the Vatican website.
Wheelchairs for the elderly are available at the museums but it would be difficult to see over the crowds in the busiest parts from that level.
Colosseum/Palatine/Forum:
Again, whether to book a tour or DIY yourself depends on how much you want to see and how much info you'd like delivered from a human versus your own research/guidebooks. Inexpensive tours of the Colosseum Underground/Belvedere offered through the official coopculture website can be a pain in the arse to try and snag as they come up for sale one day of the month for the following month, 9:00 AM Rome time (middle of the night for us North Americans) and sell out within minutes. Personally? I don't think it's necessary to see/access those extra parts but that's just me. They offer a really cheap tour (5 euro + general admission+ reservation fee) of just the arena (see the coopculture )or DIY.
http://ecm.coopculture.it/index.php?option=com_snapp&view=event&id=E6A1B5B3-BFDA-AC94-6929-0161B2E3A0C0&catalogid=23A77243-5FAB-1393-11A5-0161B2E6158E&lang=en
Palatine and Forum are different animals as a human guide can be a plus so you know what you're looking at. Again, it's up to how you want your info delivered: by a person or via your own research, guidebook or online downloaded audio to your own devices. Audioguides may also be rented at the Colosseum and Forum but I don't believe they're available for the Palatine although I won't swear to it.
A couple of details? "Open" tickets (no specific entry times or tour) are good for two consecutive days: you may visit the Colosseum on one and the Palatine/Forum on the next (those two must be visited together) or vice versa. You will not be able to skip security lines at any of these - which applies to some tours as well - and those can be long at the Colosseum. Also, "open" tickets sold on June 1, 2018 or later will not allow access to the Colosseum until 2:00 PM (14:00) or later. This is a very new development and does not appear to apply to the Forum/Palatine.
I don't believe tickets for night tours of the Colosseum include the additional entry to the Forum/Palatine on the next day.