This does work but may not be suitable if lots of data. It may help I hope.

#!/usr/local/bin/perl -w

use strict;

$/ = "FDJK";  # sets end on input line to nonsence

my $data = <DATA>;

print "$data\n\n";

$data =~ s/([^"])\n/$1 /msxg;
$data =~ s/(\w) "/$1"/;

print $data;

__END__
"data","data","data", "data"
"data","data
with new line
" "data"
"data","data,"data","data"
[download]