They're going to lose on the taking without compensation claim. The exact language of the 5th Amendment says "nor shall private property be taken for public use, without just compensation." The key phrase here is "for public use." The government is not using anybody's private property for public use; rather, they're simply telling people that they can't travel between properties.
Of everything in Whitmer's order, I see two items that are the least likely to pass constitutional muster if anybody were to actually bring a federal suit (based on something other than the 5th Amendment) on these: the prohibition on travel between residences and the prohibition of usage of motorized boats. Per a CNN article from about 5 days ago discussing the case of
Jacobson v. Massachusetts.:
Metzger speculated that "shelter in place" rules would generally pass constitutional muster but blanket travel restrictions, for example keeping all New Yorkers from crossing state borders, would not. She said the 1905 opinion should be interpreted in combination with subsequent high court decisions on individual rights.
"Jacobson stands for the proposition that (government) can take significant measures for public health," Metzger said. "But it doesn't give a free pass to regulation. There has to be a real or substantial relation" between problem and solution.
There's another case I remember reading about (can't find it now) that found something along the line of during a pandemic, emergency restrictions of otherwise Constitutionally-protected activity must be narrowly targeted at the problem and cannot be overly broad or arbitrary - and that if a Plaintiff can demonstrate that there were blatantly obvious less-restrictive ways to accomplish the government's goal, then the more heavy-handed restrictions may be deemed unconstitutional.
Applying this standard to the above restrictions I mentioned, even Whitmer admitted in both instances that these tougher restrictions were designed to limit congregation between people. I would argue that this is overly broad insofar as there were already other provisions in the order designed to accomplish the same goal - specifically, the provision banning congregations of any size. In other words, cite people for the actual offense of congregation, NOT for engaging in activity that the governor has deemed might lead to other offenses.
Whitmer might also have a problem if anybody were to bring a suit alleging violation of equal protection under the law - specifically in regards to keeping the state Lottery up and running while forcing other businesses far less likely to spread the virus to close. That whole keeping-the-lottery-open gaffe might come back to bite her if somebody uses it correctly in court.