Your receive 50% of your DNA from your father and 50 % from your mother, although in reality the ratios are not exactly equal, but near enough. They in turn received 50% of their DNA from each of their parents, but it does not follow that you received equal amounts of each grandparents' DNA. The DNA that you inherit from each of your parents is an entirely random combination of the DNA that they inherited from their parents. Consequently the amount of each grandparents' DNA that you inherit is not divided into four equal shares. You could have 40% or greater of your paternal grandfather's DNA, and 10% or less of your paternal grandmother's for instance, with a similar inequality between the inherited amounts on the maternal side.
To complicate matters further, you are referring to ethnicity ESTIMATES rather than direct familial inheritance. Ethnicity is an inexact science, being generous with the description, and the amount given by Ancestry is an estimation. So if you click on the headline figure of 12% given for your wife's North European ethnicity ESTIMATE (that word again) you will be shown a more detailed range of probability, which might explain that the estimate of 12% comes from a probability range of 0% to 23% (example figures plucked out of thin air for this example, but 0% is not unusual for fairly low estimates). In other words, your wife appears to have regions in common with Ancestry's North European reference population of up to 23% of her DNA, but Ancestry cannot be completely certain about that, and it might also be that she has absolutely no regions in common with that reference population at all, but as a result of that probability range they have come up with a figure of 12%.
So yes, such wide swings are not only common, but entirely expected, and how much credibility you give to ethnicity estimates is entirely your decision. But they are inexact by the very nature of being estimates derived from a probability range (and best not to be taken too seriously, particularly when you get into the exactness or otherwise of percentages quoted).
Additionally, ethnicity estimation is based on patterns believed to be common to general populations, not just immediate ancestors of a specific individual, so the estimated percentage/range given refers to all possibly matching patterns in the tested individuals' DNA and is not necessarily restricted to inheritance from a single parent/grandparent/GGP etc. It could just as easily be an overall estimation from combined inheritance on two or more ancestral lines. Granted, Ancestry's Sideview technology attempts to split it between paternal and maternal lines, but firstly that is a computer algorithm - again not an exact science - and it can't indicate whether a particular ethnicity shown on only the maternal or paternal side stems from a single grandparent, or both.
Ethnicity estimates are a completely different matter to segment matching between directly related individuals who descend from a common ancestor, which is a much more exact and provable science, and how we can identify people who are related to us.
