There are very good reasons to suspect that this profile is entirely fictitious.
First, because we know rather a lot about her putative parents, Magnus I and Catharine, and we certainly know that they had six children -- five daughters: Dorothea, Catherine, Ursula, Clara and Sophie -- and a son (Franz).
Dorothea married King Christian III of Denmark
Catherine married King Gustav I of Sweden
Ursula married Duke Henry V of Mecklenburg-Schwerin
Clara married Duke Francis of Brunswick-Giffhorn
Sofie married Count Anton I of Oldenburg-Delmenhorst
To recap: two daughters married kings, two married senior dukes and one married the powerful ruler of Oldenburg -- a strategic territory between Germany and Denmark. And yet we're expected to believe that another daughter, unrecorded in the Almanach de Gotha or any other source I've consulted, married some British commoner from Somerset? Not a chance!
Finally, "Minnie" isn't even a given name; it's a nickname, a diminutive of given names like Minerva and Wilhelmina. This whole profile is bogus and should be removed.
We're really talking about two questions
1) who was the wife of John Coggan & mother of his children
2) Was wife of John Cogan a daughter of Herzog Magnus I von Sachsen-Lauenburg
Let's take the 1st question first as that affects the descent field.
There's another discussion on this profile that also finds the marriage highly suspicious.
There is no reason to believe, that someone called Minnnie / Minerva / Wilhelmina was a daughter of duke Magnus I of Sachsen-Lauenburg. She is certainly a fictious person, or maybe a person, who had other parents.
Furthermore, why should a princess of a well respect ducal German family marry a rather common man in England?
I have done some research involving the ducal family of Sachsen-Lauenburg. Magnus I is one of my ancestors (great-11-grandmother).
English Wikipedia looks well sourced, I would think German even better. Nothing close to "Minnie" as a daughter and no one married an English fellow.
http://en.wikipedia.org/wiki/Magnus_I,_Duke_of_Saxe-Lauenburg
Minnie von Sachsen Lauenburg (Askanier), Prinzessin is not a historic person.
I am now changing her name to "unknown" but leaving the dates intact in hopes the name of the real wife of John Cogan will be found.