cropping and enlarging?

hi all
'ive been asked to blow up' part of a picture!
the orig part of the picture is about 2" when cropped
they would like it to be blown up to an A4(11"x8.5") to frame is this possible and still be left with a decent pic?
ive tried and the skin looks blotchy and to be honest not very good!
any advice if any would be appreciated
my workflow..scan(at 300 then tried 1200)..crop in cs2..levels..contrast.​..saturation..and sharpen (tried noise ninja too with no real quality improvement)
Is this possible they would love the pic as its the only decent one they have af there daughter as a baby..thanks

thanks for replying matt just seen that tutorial of mizunos(very impressive) i think the original pic is too small to upsize to a4 even trying mizonos tutorial i think its still an unaceptable finish..btw im not getting paid for this and gonna see if they can find a bigger photo or accept a smaller enlargement
(thought about putting it up here if anyone would like a play with it)