How can I replace a long double vanity with two single vanities?
You mentioned that you are retiling and I think your tile extends under so that doesn't matter.  
your hot and cold for each sink are already probably close enough or were they need to be.  Maybe you have to move them over a foot or two... This is an easy DIY
drain pipes for sink.  May have to move these over a little but maybe not.  Unless there is something really odd going on in the wall where you can't move a drain over a foot or two, again no big deal and maybe no issue at all.  This really depends on what kind of cabinet you get and if it has drawers that would get in the way.  
Know that your plumbing can be anywhere really.  Need to just make sure your cabinet if functional and plumbing meets code - for instance you can have your hot/cold shutoff in the corner of the cabinet if it fits there.  
Also if you do have to change these things your wall doesn't have to look perfect after with a cabinet going over.  Throw up some drywall and a bad mud job.
Maybe you get taller cabinets for the modern look?  So what you have to think about is the mirror has to go up and then possibly the vanity light.  Still moving this is taking out a couple of very small squares of drywall.  
How much space from tub?  Doesn't matter as long as it doesn't create a safety factor.  I personally would make it none or a lot (at least a  foot).  Very weird having 3-4 inches to clean there.


And my take as a cheap flipper... Tile has to go.  Cabinets aren't bad and mirror looks nice.  Paint the cabinets - maybe they need new doors.  So I might order new doors.  The counter goes.  I cut out the middle section.  I throw on granite on each cabinet, install undermount sink, and backsplash.  Right under 1K.  Can usually pick up granite and undermount sinks on craigslist as leftover or overstocks.  Your 49" is an easy find.  53" a little harder but they are there too.