Your problem seems to be that you don't have the integer-based multiplication and division implemented correctly. Let's start with multiplication:
You said, you scale both operands by multiplying with 2^14. Then you have to scale the result by dividing through 2^28. For example:
double a = 1.5;
double b = 3.6;
int as = (int) (a *(2<<14));
int bs = (int) (b *(2<<14));
int rss = as * bs;
double r = rss / (2<<28);
If you want to remain in your integer based 2^14 system you can do so by scaling the result back by dividing by 2^14.
int as = (int) (a *(2<<14));
int bs = (int) (b *(2<<14));
int rs = (as * bs) >> 14;
This way the result will be scaled also by 2^14. You can easily convert it to a double by
double r = ((double)rs) / (2<<14);
Now to division: If you want to divide two quantities that have been both scaled by 2^14, you should first scale the dividend by an additional factor of 2^14, otherwise the result will be unscaled and in your example mostly 0 or 1. Here is how to do it:
int as = (int) (a *(2<<14));
int bs = (int) (b *(2<<14));
int rs = (a << 14) / b;
Again your result will be scaled by 2^14 and can be converted back to double as shown above.
Note that in the case of 32-bit integers, you will be limited to in the number space to an integer part of smaller than 8. This is, because your initial result will be scaled by 2^28, leaving just 4 bits for the integer part, one of which is the sign bit. Hence you might consider using type long long for your integer operations.
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