In Harry Potter and the Goblet of Fire, the Pensieve is described as way of reviewing one's memories.
"I use the Pensieve. One simply siphons the excess thoughts from one's
mind, pours them into the basin, and examines them at one's leisure.
It becomes easier to spot patterns and links, you understand, when
they are in this form." - Dumbledore (Harry Potter and the Goblet of Fire, chapter 30, p. 597)
In this sense, when you view a memory, it's like watching a recording of it. So when Harry views one of Dumbledore's memories from Barty Crouch Jr.'s trial, Harry sees what Dumbledore remembers. Nothing from Harry would be contained in the memory. And Harry can't control where he goes in Dumbledore's memory — where Harry goes depends on what Dumbledore stored in the memory.
So if you found a memory of someone looking into the Mirror of Erised, you would see what the person saw in the mirror, and not what you desire. Hypothetical example: Harry stores his memory of looking into the Mirror of Erised. Ginny finds the memory and uses the Pensieve to view Harry's memory. She would see Harry's parents in the mirror, same as he did, and not whatever she would see in the mirror.
Tom Riddle's diary would have been similar. It had recordings of sixteen-year-old Tom Riddle's memories. If the diary showed the reader a memory of Tom looking into the Mirror of Erised, the reader would see whatever Tom saw in the mirror. But, since the diary was a Horcrux, and more than memory storage, it's possible it could have showed the reader something else to manipulate them. We know the diary's goal was to have the reader use it a lot, so that the Horcrux could "feed" on the reader.
So Ginny poured out her soul to me, and her soul happened to be exactly what I wanted...I grew stronger and stronger on a diet of her deepest fears, her darkest secrets. I grew powerful, far more powerful than little Miss Weasley. Powerful enough to start feeding Miss Weasley a few of my secrets, to start pouring a little of my soul back into her..." - Tom Riddle (Harry Potter and the Chamber of Secrets, chapter 17, p. 301)
But we don't know from canon if the diary could show the reader false/manipulated memories.