The tidal effect over time tends to circularize orbits. It's well known that Moon is being tidally pushed away from the Earth over time (about 1.5 inches a year). This effect is stronger when the moon is closer and weaker when the moon is farther, so there is a very gradual tidal circularizing of orbits over time, unless the orbit is highly eccentric, then you can get the reverse effect, if, when the orbiting object accelerates ahead of the tidal bulge during Perihelion that can draw it closer to the sun during that part of the orbit and that tidal effect tends to increase eccentricity.
This tidal "circularizing" only works in 2 body systems though. 3 body systems and n-body systems are more complicated. I can't explain the effect of Jupiter and Saturn because 3 body gravitation is too complex, but I can tell you that Trojan asteroids and the asteroid belt are not factors or, very very tiny factors because they don't have enough mass. orbital cycles are all about the strength of the gravitational fields any synchronization of orbits. The gravitational fields on Earth by the asteroid belt or Jupiter trojans is too tiny.
The temperature change on earth can be observed by the ice ages. The net effect of the Milankovich cycles, if the earth was consistent would be quite small, maybe 1 degree C peak to trough. Most of the 10 degree change globally that we see, ice age to warm period between ice ages is due to feedback mechanisms on the earth, glacier formation and ice cover increases albedo which reflects more sunlight directly back into space and colder oceans absorb more CO2 which lowers the greenhouse effect and as glaciers grow high the air over high altitude gets colder. Changes in ocean currents may be factors too, but that's not as well understood.
Locally, the effect can be much greater than 1 degree C though, even without the feedback mechanisms. Precession has much more significant local effects because 3.4% closer at Perihelion means 6.8% more energy, and that's significant, even if it varies, 3.4% above normal peak summer to 3.4% below normal, low winter, but that's enough to cause a significant change. It's thought that precession is behind the Sahara desert cycle between forest and desert every 13,000 years or so. Precession may be (speculation on my part), a factor in ending ice ages as well, but it doesn't seem to be a factor in starting them, as ice ages appear to begin on roughly 100,000 year cycles and before that, 40,000 year cycles. Source. There's not any good evidence that I know of for ice ages operating on 26,000 year cycles.