Seems we have a bit of a language problems here. Let me try again.
First, we have to recall John's love of witticisms and puns. Remember, he's the guy who wrote A Spaniard in the Works. The original idiom for the title is 'a spanner in the works'. A spanner is a tool, while a Spaniard is of course a man from Spain. The two words (spanner and Spaniard) have nothing in common except for sounding somewhat similar. That book (A Spaniard in the Works) is filled with idioms given the John Lennon touch.
So, in "You better see right through that mother's eyes" we deal with at least two idioms; 'see right through' and 'see through a mother's eyes'. A third, 'to see right', meaning to correct or help [somebody], could also be implied.
To see right through means to ignore, pay no attention to. Through a mother's eyes means to hold cherished illusions about something dear to you or your creation. Properly it should be 'you better see right through through that mother's eye' but that's a very clumsy way to expressing it and it also leaves out the third idiom. So John eliminated the second through and we're left with the line above.
Thinking further on the first line "So Sgt Pepper took you by surprise" it's probably a reference to something said by Paul in an interview. Paul has always credited Sgt Pepper to himself. And it's true, the original idea was Paul's and he contributed to it but he has exaggerated his role. That's what John's getting at. If so, the second line makes even more sense.
In plain English then, the two lines would read something like: So you're taking credit for Sgt Pepper and its success. Well, you better correct that cherished illusion. It also ties in well with the rest of that that verse, in particular "The one mistake you made was in your head."
Sometimes I dream in colors
It always happens when
I find myself with others
Who don't pretend