It is a small planet in a long oblong orbit around its sun. It has two satellites. One large moon (nearly the size of the planet) and a smaller moon with which the larger is tidally locked and causes irradic affects on the planets rotation.

Our moon is big enough, that in actuality, earth and the moon are not really going around each other, but on a wobbly path around the sun in sync with each other. the center of gravity is close enough to the surface of the earth to make them both in orbit around the sun. If the earth suddenly disappeared, the moon would never be in retrograde around the sun. It might shoot close to the sun or out into space, but never in retrograde.
A smaller moon, such as one around mars, orbit near the center of the planet. When it goes around the front of the planet, it is actually going retrograde to the sun (Of course, farther the planet is away from the sun, the more pronounced the effect is) If the small moon was going in the reverse phase of the orbit, and the planet disappeared, the moon could end up orbiting the sun backwards.

What is sounds like you are trying to do, is to have a three gravitational object situation. I don't think that computers have quite figured that out yet. Three somewhat equal objects in gravitational interaction, end up giving you some radical orbital weirdness. About the only way to have three objects in orbit together, is to have two close together essentually following the same orbit, something like our moon. Then have the third much farther out, orbiting the gravitational center of the larger two. Then of course, there are those places, I forgot the name, where gravity between the sun and the planet, are the same. We have satellites orbiting those points. They are almost stationary in space.

Seasonal variations on Earth are primarily a result of axial tilt; secondarily, a result of proximity to the Sun. Seasons in the southern hemisphere experience a greater range of temperatures than the northern hemisphere because summer occurs at perihelion, winter at aphelion. Northern winters and summers are milder than in the southern hemisphere.

A highly eccentric orbit would, of course, result in similar but appreciably greater perihelion/aphelion extremes. How much axial tilt would also be an influential factor.

In imagining a dual satellite system, the simplest way to visualize it is to perceive it as a two system body within a larger two system body. The two moons are a two-body system that is one of the two bodies in the larger system. The two bodies of the larger system would orbit in a braided path. The Earth and Moon do with the actual motion of the Moon being more eccentric than the Earth. It's a spinning dance of two partners holding invisible hands across space; Earth, an adult; the Moon, a child. Simplified models give most people a perception that the Earth orbits in a flat ellipse, but it doesn't. Earth's orbital aberration is on the order of 1:6 of the Moon's aberration.

The smaller moon orbiting the larger one, assuming it's gravitationally bound, would need to be small enough where it wouldn't be appreciably disturbed by the planet's gravity. So small that it wouldn't have an appreciable influence on the larger moon's orbital motion.

If a visual representation is wanted, Celestia is a freeware astronomy program that allows for creating imaginary solar systems. In order to learn how to create imaginary systems, there's a huge learning curve involved in learning the Celestia scripting language and the basic orbital dynamics involved. A digital imaging program is needed, plus, perhaps, a 3-D rendering program for creating the models for the planets and moons. I run Celestia on a laptop with 2 GBs of RAM. Lower memory systems didn't run it as well. I use Anim8or for creating models, and Corel Draw suite for creating textures and image rendering. Barring creating imaginary systems, Celestia is a fascinating astronomy program otherwise.

Even if the moon was tidally locked, like our moon, and the satellite orbited at a parallel plane, the planetary gravitational pull would draw the satellite into a perpendicular orbit with the planet and then pull it away from the moon. This situation could exist for a short time astromically (maybe a couple hundred thousand years), but it could also be detrimental to the existence of life on the planet (asteroids, tidal affects, and other problems would likely destroy life).

Here is the site I found that best explains why this situation would not work for long.

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Then of course, there are those places, I forgot the name, where gravity between the sun and the planet, are the same. We have satellites orbiting those points. They are almost stationary in space.

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The Earth is, more or less, on a circular orbit around the sun, with the closest and farthest distance between us and the sun (perihelion and aphelion) at about 147 and 152 million km, respectively (pretty similar). This is why the axial tilt is necessary to cause seasons. If there were no tilt, it would be pretty much the same temperature all the time at any given location on the Earth.

In elongated orbits, it is important to remember that the sun is at one of the foci of the ellipse (not at the "center"), and planets move much slower in their orbits when they are farther away from the sun (Kepler's Law: see http://en.wikipedia.org/wiki/Kepler%27s_laws_of_planetary_motion for example).

As a consequence, planets like this will spend most of their time far away form the sun, receiving little light/warmth, and will freeze over. The various temperature changes on the Earth will seem like nothing in comparison. Without knowing the specific eccentricity you want for your world (if you are unfamiliar with the term eccentricity, http://en.wikipedia.org/wiki/Elliptical gives a decent description).

I can't really give specifics, but consider the following as qualitatively plausible: a planet where winter lasts something like 70% of the year, during which time temperatures reach very low temperatures (I'm pulling numbers from nowhere here, but let's say -100 F), with the other 30% of the time being spring/summer/fall (and summer will be the shortest of these seasons). Also keep in mind that since summer only happens at one specific place in the planet's orbit (perihelion) is is completely plausible that, if the planet has significant axial tilt, only one side of the planet gets to actually face the sun during the short summer time. This could be a good thing or a bad thing for this side of the planet. While most of the year is freezing, it's possible that this summer could be closer to the sun than Earth's own orbit, causing extreme heat for this short time, beyond the boiling point of water.

There's a lot of variables to play around with here, even without the added complexity of 2 tidally locked (to each other?) moons. Of course if you want a slightly eccentric orbit but not something so extreme, the effects will obviously be smaller. In simplified terms you can think of it as, "the more eccentric the orbit, the more extreme the seasons will be, both in temperature and in length, with winter getting longer and summer getting shorter for eccentric orbits."

The bodies revolve around each other in a way where they eclipse for long periods of time, once a year, causing a second winter

One thing to think about, is that one could have where one of the objects was recently captured. LIfe, that was on the planet, would still exist, though you might not find creatures even the size of hippos. there would be signs of recent upheaval.

It would not be a permanant arrangement but could be stable enough for the story you are telling. Even a hundred thousand years would be a long time for life and your story, if these are colonists. Even a few thousand years would appear permanant if you did not know any difference (one theory says that our last global extinction event, with major upheaval, happend within the past seven thousand years. if that were true, then one would never know anything was different in millions of years. I also read that some soviet scientists deduced that a solar system such as ours could not possibly be stable for longer than a million years).