The American mom and daughter would win. She's a world class Judoka and her daughter won an Olympic Judo bronze medal and is going into MMA. Probably need a more neutral event then wrestling :)
I'm a VP of IT at my company and I have an Aerospace Engineering degree. The only distinction that I can say between problem solving with an engineering background versus a CS background might be the breadth of the tools you have to solve your problems. Many times, I noticed programmers do a great job of solving problems, but they are only able to use the languages they know best to solve them. As an engineer, I felt that I was, mentally, more free to solve problems with out-of-the-box ideas. I don't believe there is a book or write-up that can help you there though, other than experience and the willingness to open up your mind and research solutions outside of your normal expertise.
Can you cook? If not, learn. Cook new stuff and invite neighbors over for dinner and get to know them.