Driving/insurance

Hello!
My wife (UK resident) and I (USA resident) just bought a car here in the UK, and we want to buy insurance and put me as the 2nd driver.  I called Direct Line and Cooperative and they both declined because I have a US license.  I am here on a spouse visa. 
I researched getting a UK license but it says that I have to be a resident to get one.  I am so confused of how to go about getting to drive in the UK, someone help!

You are a resident of the UK. So just get started on getting a UK license. First step is to apply for a provisional license.  And if you moved to the UK in March 2013, you only have another 3+ months to drive on your US license, so get on it.

Thanks Geeta.  I actually left a bunch of times to go back to the US, so I came back a few weeks ago...does the one year start last time i came in and out or did it start when my visa was issued?

The driver manual says you need to have been a resident for 185 days of the last 12 months, but I'm not sure that's consecutive. 
You may want to check around to other insurance agencies.  I just asked some friends and they said that they were allowed on their spouses policies even with a US license. 

It starts when you moved over to the UK. It doesn't matter if you took trips out. Basically the first time you came over on your spousal visa.

I came to the UK on a work visa (so no UK citizen to attach myself too) and was able to get car insurance (I went with Admiral).  You will pay slightly more.

But yes, get on your UK license ASAP.  I took my written test in August and the first available driving exam was not until December. 

As Geeta says you have only until March.  After that you'll have to follow the learner driver rules as your insurance will no longer cover you as a fully licensed driver.