So basically I misread the motor curves spreadsheet that I posted earlier in this blog. I believed that the motors would run at 15A usually, however, little did I know that this was at the most efficient running of the motors. As we all know, life is far less than peak efficiency and so it was more likely that the motor would run at 50A at times. So long story short, RTFM. Read the datasheets veeeerrrry carefully.
Second part which pretty much illegitimises the first part. Forums are a spectacular place, especially engineering forums. Odds are there's always someone who has done what you're doing and can help you a great deal. That being said, there are also a lot of unhelpful people who make relatively meaningless posts. Nonetheless, it's still very important to carefully and fully read any threads that you may be looking at or that may be related to your project. This was the case for the datasheet. It is contained within a robotics forum, and only the first post. The posts later in that thread, which I neglected to read until my first H Bridge had gone up in smoke, discussed the unlikeliness of much of the data that the motor curves showed. It showed that the motor peaks at 150A which is a HUGE amount of current. I eventually proved this illegitimacy to be true, as will come in a later blog post, but the reality is that the current drawn is far less than that.
In addition to reading through datasheets and forums, it's also a good idea to use your own judgement most of the time. For one, the fuses on the stock power wheels batteries where 30A. That alone should tell me that even the stall current (peak current) would be less than that. And two, 150A running through the stock 14AWG wire would definitely start melting some things. Considering that this is a children's toy, these dangerous conditions and amounts of current should have thrown up a read flag in my head, telling my that these were unlikely. All in all, it's a good idea to make sure that your research is thorough so you don't make stupid mistakes like I do.
As for soldering, my circuit board is ugly, as most of you can see. I used a knife to widen the holes so I could fit in a bigger gauge wire, in addition to an overall poor job of soldering with an old and very worn down iron. A good soldering job takes time and a lot of practice. Beautiful solder joints also show professionalism. Since I am not qualified to show a soldering tutorial by any means, I'll just post a link to a very nice tutorial by the people over at sparkfun. http://www.sparkfun.com/tutorials
They have a nice soldering tutorial in the bite sized primers section, in addition to many other good tutorials on basic electronics knowledge. And now that I've gone over more of my faults as an electrical engineer, it's time to go study for a test.