If I were in the OP's position, I'd concentrate initially of sorting out the cab. At the amp shootout at the last SW Bass Bash, we tested and compared a range of low powered mini-heads through an LFSys Monaco. At one point, one of the amps was driven into clipping to see how loud it would go. There's no doubt that they all produced an SPL that was more than enough for your average pub/club gig. So I wouldn't worry too much about the amp at this stage, although it's always nice to have more power on tap.
"The sound is very muddy and lacks definition (and that's when I'm able to hear myself in the mix)."
I'm afraid that's what cheap cabs sound like. To get to a low price point, manufacturers specify drivers with small magnets and small voice coils, which distort easily and tend to produce a one-note bass. If you buy a second one, you'll still have a muddy, undefined sound - but louder. You might be able to hear your self a bit better by virtue of the fact that the second cab is closer to your ears.
As @Dan Dare advises, you need to try out some more cabs. Don't rely on forum recommendations. If money's tight, go for a used 15" cab made by a decent brand. Fifteens have fallen out of favour nowadays and can be picked up for very little money. A decent fifteen will do the job for you. As far as hearing yourself is concerned, try turning the midrange control up on your amp, or tilt the cab so that it's directed towards you.