MCP6N11 reference voltage problem
Well, I don't see anything explicitly wrong with what you are doing in your circuit with Vref = 0.  But there are some concerns.  Looking at the datasheet for the MCP6N11, nowhere do they ever set Vref to zero.  All of the specified performance is for Vref = Vdd/2, or Vref = 0.75Vdd, or Vref = 0.25Vdd.  None of the sample application circuits show Vref=0.  Although the limits for Vref are stated as between \$V_ {\text {IVL}}\$ and\$V_ {\text {IVH}}\$, I could find no spec or example where they got outside 0.25Vdd or 0.75Vdd.  It is suspicious.  

I wonder why you use the 33 kOhm and 10 kOhm dividers on the inputs.  Is the battery voltage larger than Vdd, and you are trying to keep the common mode voltage (Vcm) within spec? Usually one of the advantages of using a instrumentation amp is not having to use dividers.  The problem is that tolerances add up quickly, and usually 1% resistors are not good enough to give adequate performance.  For example if Vbat = 10V, 1% resistors could give an input voltage variation of +/-36mV.  With a gain of 100 this could easily put you with an output voltage below Vref.  

So, if you are going to or have to use dividers on the input it is crucial that they be very tight tolerance, or trimmed for tracking.  You can find special parts like this (tight tolerance and trimmed), but they are somewhat special items.  For a trimmed part with 0.1% tolerance and 0.01% tracking, you might spend $2 per divider.