Your best option would be to have your daughter contact her insurance company about possibly adding you as a driver to her policy for the 2 week timeframe. They may not even require that you be listed since you will only be driving temporarily, but she will need to check with her company on the specifics of covering you.
The length of driving experience that insurance companies use to determine your rate is based on US driving. Your previous experience may slightly improve your rate, but the length of time you have been licensed in the US will matter the most.
Even if you don't have a US driver license, you should still be able to find coverage with most insurance companies. You mentioned that you will be traveling around the US so it's important to note that US insurance companies require a "permanent" address before they will issue a policy.