taking three seniors to Monserrat Monastery: should we book a tour or try to go on our own?

This is easy to do on your own, I did in 2010 on the tail end of a business trip following the instructions in my Rick Steves guide book. If there are mobility issues, I am not sure a tour solves that for you. If it's just logistics that you are concerned with, really the logistics are not that hard.

If you get to the train station in Barcelona, there will be automated ticket machines to buy your ticket. Bring cash as the ticket machines didn't take of our credit cards. The signs are a bit confusing to get you to the right train but Rick Steves books tells you how to find it. As I recall we did have to ask someone but then followed the crowd. Once you get to Monserrat, it's rather difficult to get lost as you will see the Monastery when you get out of the train station, plus there are helpful signs everywhere.

My advise is to do it yourself as it allows you to bypass things you may not want to see or do. We decided to skip the Virgin Mary line and spend more time hiking as it was a beautiful day.

I'm assuming from Barcelona? A bus will drop you right by the church. Much less walking and less chance of getting lost. I'd choose that over a train then navigating to the sight. Any of the bus stations and/or TI will have bus tours that will take you there, give you plenty of time to visit, then take you back to Barcelona afterward.

This is a perfect summary of how easily Montserrat can be done on your own.

https://community.ricksteves.com/travel-forum/spain/a-visit-to-montserrat-the-holy-mountain-near-barcelona-in-catalonia

Thanks to everyone for your advice! Even though the bus is easier, I think we'll be adventurous and try it by ourselves! The thought of taking the train just sounds too good to pass up!