Giant stars are very unstable and short-lived. And the yellow giants are perhaps the most short-lived phase of the giant stars. Being a yellow giant, puts the star in the instability strip. Also it may turn out into a blue giant or a red giant in something like just a few millenia or even during a person lifetime (see here).
A yellow giant star is incredibly bright, while a red dwarf is incredibly dim. This means that the red dwarf and its planet would be orbiting the yellow giant in a very distant orbit.
For comparison, the Sun is a yellow dwarf, so replacing it by a yellow giant would mean that the planet would be much far from it to receive the equivalent illumination and heat. Add a very close red dwarf and this means being yet farther.
Further, all of the known yellow giant stars pulsate wildly and violently. So, whatever are the desired conditions on the planet, they likely won't last long.
Seen from the surface of the planet, the yellow giant would be like the Sun, raising somewhere in the horizon and setting somewhere else after roughly 15 hours. There are some considerably possible scenarios here because the planet could have any inclination in its rotation regarding to the yellow giant. Also, depending on what this inclination is, the red dwarf could eclipse it daily.
The hottest part of the surface would be likely those that where the two stars are visible in sky, preferable near the zenith. The coldest part would be the night side (i.e. where neither star is visible). Since it is tidally locked to the red star, this mainly depends on the planet's axial tilt regarding to the yellow star.
If this axial tilt to the yellow giant is low, which also means that the red dwarf eclipses the yellow giant daily, the hottest place would be in the sub-red-dwarf spot just before of just after the daily eclipse. During the eclipse, the side of the planet facing away the red dwarf is experiencing night, and the polar regions at the night would likely be the coldest spots.
If the axial tilt is high and the planet is at an equinox regarding to the yellow giant translation, eclipses would happen daily and the days would resemble those of the small axial tilt.
If the axial tilt is high and the planet is at a solstice regarding to the yellow giant translation, roughly a quarter of the surface would have two suns in the sky, roughly a quarter only the red dwarf, roughly a quarter only the yellow giant, and roughly a quarter will be night. However, due to the atmospheric thickness and the great angular size of the red dwarf in the planet skies, there would be also large areas of dusk around the night shade which. So the night would more likely cover something around 15% to 20% the surface rather than a quarter of it.
However, since the planet and the red dwarf have a very long and very slow orbit around the yellow giant star, likely of some millenia at least, this means that the planet might never experience a full giant-yellow-year while being able to maintain your desired characteristics due to that star instability.
In general, heat, and with them winds, tends to go from the hotter places to the colder ones. Since the planet have few exposed land areas, this also means that the effect that differences in land airs and ocean airs become much less significant, since there would be almost no land air. Also, this likely means that there are few to no high mountains acting as wind barriers.
The air is thick and due to that it is efficient in transporting heat. Most of surface are oceans, which also helps in keeping the temperatures more uniform. The air thickness also contributes to reduce the influence of ocean currents.
So, if the planet has a large axial tilt and is in the solstice regarding to the yellow star, this means that the heat will flow from the place that sees both stars to the night side. The air is likely very humid and the place seeing two suns will evaporate a lot of water, which will rain as severe storms or typhoons in the night side and sometimes in the middle of the way to there, where only one of the stars is visible.
The planet temperature would not variate too much, because the water and the air would efficiently distribute heat around the small globe.
Land areas that are always facing the red dwarf are likely to become desertic. The waters on those areas evaporate and tends to rain down very far from there. The winds would be rushing away from that area, so it would seldom receive rain. Also, a permanent sun in the nightless sky with possibly two suns sometimes would also contribute to make that area very dry.
An ice cap could likely form only if a part of the planet is experiencing polar night from both stars. This mainly depends on the axial tilt to the yellow giant, since it is tidally locked to the red dwarf. This ice cap would likely also experience snows and blizzards.
In fact almost all of the wind patterns could be derived by the position of the stars in the sky and mapping which areas see two suns and which areas are night. Ocean currents and continental masses are likely being too small to influence for something relevant.
Volcanic activity might disturb the weather patterns, but are only being a minor influence. They either creates large areas of warmer waters or throws a lot of ashes in the atmosphere which might block some sunlight and decrease the global temperatures a bit.
