Getting the permit isn't difficult, your wife just needs to apply for a dependent's permit for you. It should also include work rights as you will have the same type as she has. You will need to apply for a Type D visa at the nearest Swiss embassy/consulate to where you live so you can enter Switzerland long term legally. https://www.ch.ch/en/family-reunification-eu-efta/
The problems may come from the self-employment/taxation sides. On the self-employment usually as a contractor I think the Swiss authorities would want to see more than one client for you to qualify, otherwise they'll still consider you an employee of your US company. I suggest you contact the Zurich taxation office to find out whether it would be possible or not as technically what status you are defines who pays what for some insurances/taxes. http://www.steueramt.zh.ch/internet/...a/en/home.html
More self-employment info here: https://www.ch.ch/en/becoming-self-employed/ http://www.kmu.admin.ch/kmu-gruenden...x.html?lang=en
Tax-wise, yes you will be able to offset/exempt some of the Swiss stuff, but you'll still need to file US tax returns and could owe US tax on top of Swiss ones. Start researching here: http://www.irs.gov/Individuals/Inter...-Aliens-Abroad
At the Swiss end you could also hit problems. Due to the US's FATCA law US citizens are no longer welcome here at many banks so your choices are limited: UBS, Credit Suisse, PostFinance and the cantonal banks of Basel and Zurich are just about it. You and your wife's accounts will also need to be reported on an annual FBAR form if the aggregate total comes to more than $10,000 at any time of the year. You and she would also need to sign a W-9 form to allow any Swiss bank to pass your account info on to the IRS. And more importantly for your business side no Swiss bank is likely to give you a business account I'm afraid. Nor mortgage or investment accounts.
Depending on your wife's salary and what you earn you would probably need to file a Swiss return each year if your joint income is more than CHF120,000. The Swiss don't do individual returns, only filing jointly so both incomes would be taken into account when deciding what tax you'd pay.