I’m reasonably confident it is but I’ve had several others express doubt.
My daughter 15yrs, 7mos has had her Wisconsin learners permit for a month now. She, her 17yr old brother and I are headed out of state next week. Is it legal for her to drive in any of Illinois, Iowa, Missouri, Minnesota? Assuming I stay sober as the law requires in Wisconsin.
Yes you are not a lawyer and this is only advisory.
Yes, all drivers licenses are portable, and valid in every state. She will be subject to the accompaniment rules of Wisconsin, so be sure you know who can drive with and whether passengers are permitted in your own state… However, she might have to be driving a WI-plated car to enjoy that privilege. Portability may not carry over to a car with Illinois plates while driving in Illinois, that falls under different rules of jurisdictions. (All the above my opinion based on limited experience and common sense.)
Edit – It might not be loegal, even in WI, for her brother to be a passenger in the car.
Learner’s permits are not drivers licenses and are not valid in every state. I don’t know the laws of the states in question, but I know they’re only valid in some states and not others.
Wisconsin allows immediate family members in the vehicle along with the adult supervision requirement. Iowa and Illinois allow passengers up to the seatbelt limit with the adult.
That’s not an accurate application of the law throughout the country. New York, for example, requires that every motor vehicle operator, whether learner’s permit or licensed, be at least sixteen. (NYS Vehicle and Traffic Law § 503(2)(d) et seq) It’s not permitted to drive younger in New York, even if you have a learner’s permit from another state.
As to the states that the OP mentions, a quick bit of research suggests that Illinois, Iowa, Missouri, and Minnesota are probably willing to recognize an out-of-state learner’s permit for a driver who is 15 year seven months old, but you should contact each state’s Highway Patrol / State Police to confirm that this is the case.
Call the appropriate State Troopers to answer that question. They will know the law & give you good advice. Most State troopers have a toll free number that you can call them on. Or, there is this thing called the internet, I hear that the troopers are on that as well. 
Years ago, my niece drove from Maryland to Maine on a learner permit (supervised by her parents) without ever considering that it might not be legal. I had my doubts and found a site similar to this one that says it was legal in all the states she passed through except Pennsylvania. Luckily she didn’t get caught in Pennsylvania.
Keep in mind that a learner’s permit is exactly that, and is not intended to be “a license to drive” for the general purposes of operating the family car on family travel. Its purpose is to give a learning driver an opportunity to get practice while being supervised and instructed by an older experienced driver.
Now that the route is planned, I figure her to drive in Wisconsin. We are traveling mostly overnight so most of the out of state travel is outside her authorized driving hours. Since my son is on his graduated license yet, they are also outside his hours. I just thought this would give them the [del] joy [/del] opportunity to city drive through Chicago.
How hard is it to check with the DMV in each state you are concerned about and find out for certain?
My understanding, and I freely admit it is ad hoc, is that a learner’s permit is valid only in the state where it is issued. That is certainly what the driving instructor indicated when our son had a learner’s permit. Of course, he was learning to drive in the state of Hawaii, which is atypical in many ways. But speculation is pointless when a clear answer should be easy to acquire.
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Sure, but what if he accidentally drove across state lines?
He’d get wet?