Newer iPads are about 16 times faster than your five year old Gen 1 model. . . and 8 times faster than your wife's gen 2. They are all 64 bit now too, compared to both of your 32 bit models.
I'd suggest selling them for what you can get for them and upgrading. Google's YouTube deliberately discontinued support for devices older than about two years old last year. They even dropped support for my 3rd generation Apple TV and pulled their App. This was NOT Apple's choice, but a decision made by Google. I have heard you can still look at YouTubes on the web using HTML5, though, but I cannot testify to that of my own experience having taken my own advice and upgraded. My girlfriend's 2nd Gen iPad works fine just as your wife's does. . . but with Google's attitude, who knows how long that will continue.
I can watch Youtube videos by going to m.youtube but I have to search for the video. Too involved for me.
If I see something I really want to watch I find it on my MBP and open it.
I think the biggest problem I have surfing w/ the Gen 1 is the video ads that automatically open and run when you go to a site.
That is a fairly new addition to the chaff.
Really really annoying.