Answer: You are basically correct. You are the “I” (individual) in the term “IRA” (Individual Retirement Account). Because IRAs are qualified tax deferral investment vehicles, you cannot transfer them to a trust. Any attempt to liquidate the IRA will require a significant tax payment. There are still planning options.
If we accept the fact you are “stuck with your IRA”, perhaps don’t double the risk by leaving it to your wife. You have an opportunity to redirect your beneficiary designation away from your wife, and protect the IRA funds for your kids – in case your wife needs nursing care. Note: this scenario assumes you pass away before your wife (this is certainly my plan).
What is the downside?: Naming your trust as beneficiary may protect the assets but, doing so will end your IRA based tax deferral. Upon your death, there will be significant taxes paid from your IRA, because unlike individuals, a trust cannot benefit from an IRA. Consult with your CPA to determine the tax effect of naming your trust as your beneficiary.
Possible offset to the tax effect: Instead of naming your trust, you can name your two children to receive the IRA funds in their own names. This allows them to continue tax deferral for a certain period of time. However, it also subjects the IRA funds to your kids creditors (ie: death/divorce/taxes, etc). Because your wife will have no control, you better trust your kids 100%.
Ultimately, there is a tradeoff to be decided here: do you prioritize asset protection at the cost of a large tax bill upon your death? Explore further with a trio of professionals: Financial Advisor, Tax professional, and Attorney.