I got the rear cassette changed to an 11-32 but it does let me go into 1st or 2nd gear when the chain is on the large cog at the front. . . . when I try to change it just rubs
Shimano spec
I assume you have the GS version of the RD-4700 as the SS (short cage) version is spec'ed to max 28t sprocket.
I read this as the front derailleur (FD) not being indexed correctly. As the OP changes up the cassette it gets to a point where the chain rubs on the inner cage plate of the FD. If this is the problem you just need properly to index your FD.
I assume the chain does go on the largest sprocket (at the back) when the chain is on the small chainring (at the front)?
It is possible, though, that if the chain was already a bit short with the 12-28 cassette on, the chain would just be too short for the 32. But it should at least go on the second largest which will be 27 or 28 (which is another clue as to this not being a chain length problem). Only one more link (one inch) is needed if the length was right with the 28t - but best to get the length right from first principles, as others have suggested.
AASHTA
When on the large ring and the third largest rear sprocket, what o'clock does the cage (with the jockey wheels) on the rear derailleur (RD) describe (eg 5, 6, 7)?
Finally, you probably need to screw in to its fullest extent the 'B screw' (the end of which presses against the hanger and tilts the RD). When in the largest sprocket, the top jockey wheel should be circa 8mm minimum below the large sprocket teeth.
Since you presumably have 4700 STIs as well, you may wish to scan
this thread on woes with 5700 (same under bar tape cable routing).