Forgive my ignorance, I'm out of my depth.
My wife has pointed to the upsurge climate and geological activity post Eclipse. My immediate response, at least inwardly, was to reject her suspicion. However, the tectonic plate shift yesterday, in Mexico was substantial and the constant interplay of nature's habits seems more robust than usual.
Is there substance to her hypothesis / theory, that the Eclipse and recent events on Earth are interrelated?
The occurrences of Hurricanes, Harvey, Irma, Katia and Jose, east of Mexico and a magnitude 8.1 earthquake southwest of Mexico within a few weeks of the American solar eclipse of August 21, 2017 are purely co-incidental.
Hurricane Katrina, which devastated New Orleans in 2005 was not associated with any type of eclipse - solar or lunar.
Likewise the eruption of Mt St Helens in May 1980 was not associated with any type of eclipse, or were the San Francisco earthquake of April 1906 or the Loma Prieta earthquake of October 1989.
There is a list of every solar eclipse that occurred globally during the 20th Century. From the list, you will see there were one to two solar eclipses every year during the past century. None of these have ever been associated with any natural event such as earthquakes or hurricane/cyclones/typhoons.
Co-incidences in nature occur all the time.
While Knobscratcher's answer is technically correct that there may be some correlation between the Moon, Earthquakes and Ocean currents and Weather that lead to Hurricanes, that correlation is not confirmed, it's only been determined to be possible and to make a direct correlation is pretty thin.
What's more, a Solar Eclipse is not only fairly common but it's not a peak tidal tugging event. There's no reason for a solar eclipse to be any different than any other period in the Moon's orbit.
Certainly throughout history it was quite common to believe that eclipses or comets could forecast destructive events. This belief, for obvious reasons, waned when better understanding of the orbits of the Earth and Moon explained why eclipses happened and made them predictable but it's natural, if somewhat unscientific, to try to make a correlation.
There's about 70 per century and if we include partial and annular, over 200 per century. See: 20th Century and 21st Century. Eclipses are common enough that natural disasters following eclipses shouldn't surprise anyone. It's statistically curious that an Eclipse, 3 major hurricanes (4 if you count Max that hit Mexico, but I don't think that was major), and two major Earthquakes all hit North America over a few weeks. That's curious, but there's basically zero good science that ties all those events together in an armegedonish kind of way.
Hurricanes are often be very seasonal, where optimal conditions can lead to greater hurricane formation. Hurricane formation is complicated, and I'm not an expert, but this article touches on some of the basics - scroll down to "Why is this season so active"
Factors like a strong west African monsoon and consistent wind speeds surface to 10 miles up and warm oceans (that much is partially due to climate change), and a neutral El Nino. These are factors that can make a hurricane season more or less active and a strong hurricane season was predicted months ago.
Earthquakes operate differently, usually building up gradually for years - and like a very slow game of Jenga, when the pressure surpasses the resistance holding the ground in place, you get rapid movement. It may be theorized that hurricanes and weather may occasionally trigger Earthquakes, but the potential for an Earthquake still needs to be there in the first place and to say the "wind and rain did it" is still pretty tenuous. The two Mexico quakes happened along the Ring of Fire where Earthquakes are fairly common and one following another a few weeks later is also not uncommon.
To say there's no relation is perhaps not the scientific thing to say, but it's very likely that there's almost no relation between the active hurricane season which was anticipated before it happened, due to the right combination of ocean and weather pasterns, and two Earthquakes in an Earthquake prone region, where Earthquakes are expected to happen every several years to couple of decades. And these two events are over 1,000 miles away from each other. (unless you count Hurricane Max which was closer to the Earthquakes but just a category one).
Coincidence is the most logical answer and tying the eclipse to these events as well, any correlation there is to thin to contemplate.
There is precedent for believing that an extreme weather event can trigger seismic activity. There's also solid evidence linking tidal forces (lunar/solar cycles) to plate boundary slip.
It's totally reasonable to think that accumulated repeated tiny stresses, particularly on our dynamic planet, can contribute to the final straw that releases a large seismic event.
So... to answer the OP,
Is there substance to her hypothesis / theory, that the Eclipse and recent events on Earth are interrelated?
The answer is, "maybe". It'll take a couple of graduate-student-years before all of the necessary data is processed, analyzed, argued-over, re-analyzed, submitted, reviewed, edited, and published. If you're interested here's a few papers that your wife will find relevant and fascinating. I also urge you to look over the references at the end of each paper to see how much work has been done in this field by people unwilling to brush off observation as mere coincidence. The first article is a useful starting point:
More Evidence That the Moon Contributes to Earthquakes
Ide and colleagues noticed the Dec. 26, 2004 Sumatran earthquake, most notable for its horrendous, deadly tsunami, occurred near the time of full moon and spring tide. So did the Feb. 27, 2010 temblor in Maule, Chile. These quakes both happened close to the peak of tidal stress, when the moon and sun teamed up to exert the greatest gravitational influence over Earth.
An integrated perspective of the continuum between earthquakes and slow-slip phenomena
We find that slow-slip phenomena are not unique to the depths (tens of kilometres) of subduction zone plate interfaces. They occur on faults in many settings, at numerous scales and owing to various loading processes, including landslides and glaciers. Taken together, the observations indicate that slowly slipping fault surfaces relax most of the accrued stresses through aseismic slip.
Tidal modulation of slow slip in Cascadia
We find modulation of the strain rate with a 12.4 h period, that of the tide with the largest amplitude, that is significant at the 99% level. The amplitude of this modulation suggests that the slip rate during slow slip events oscillates, on average, 25% above and below its mean value during a tidal cycle.
Correlation of tremor activity with tidal stress in the northern Cascadia subduction zone
Tremor activity during five consecutive ETS events beneath southern and central Vancouver Island correlates significantly better with tidal shear stress and compressive normal stress on shallow dipping surfaces than with tidal confining stress.
Slow earthquakes triggered by typhoons
Here we show that, in eastern Taiwan, slow earthquakes can be triggered by typhoons. We model the largest of these earthquakes as repeated episodes of slow slip on a reverse fault just under land and dipping to the west; the characteristics of all events are sufficiently similar that they can be modelled with minor variations of the model parameters. Lower pressure results in a very small unclamping of the fault that must be close to the failure condition for the typhoon to act as a trigger.
