How do Full Preterists interpret 2 Peter 3:9-13?

Here I am assuming 2 Peter was written pre-70. If it wasn't written pre-70 (many scholars think it was written later), then it wasn't written by Peter, who died in the 60s.

For the preterist view, I am going to look at preterists who think this was fulfilled in AD 70 with the siege and then destruction of Jerusalem, including the deaths of 100,000s of Jews, enslavement of many more, toppling of the established Jewish religious order, and destruction of the 2nd Temple which was the centre of Jewish worship.

This description in 2 Peter is interesting because it is so sensory. There are a few parts that stand out, which the OP has bolded.

• the sky|heavens will disappear|pass away with a roar
• the elements|heavenly bodies will be burned up and dissolved
• the sky|heavens will be set on fire and dissolved
• the elements|heavenly bodies will melt in the heat

The overarching theme in 2 Peter 3 is the destruction of the old heavens and earth, and creation of the new heavens and earth. But there is an emphasis here on fire - burning up, dissolving, and melting.

Although a preterist could say this is all symbolic, hyperbolic talk, in line with apocalyptic Biblical language (see the answer here for more on this idea), including where the heavens are associated with the rulers (see the answer here for more on this idea), it might be worthwhile to note the use of fire in AD 70. Here, I am drawing on 2 Peter 3:5-13: A Preterist Commentary.

"As part of the Roman scorched-earth policy, Josephus records the fact that the Romans literally destroyed the cities and much of the countryside of Israel, the earth, by fire during the Jewish War."

The use of fire to describe the events involving Jerusalem and Judea in AD 70 is appropriate because, indeed, the Romans used fire extensively.

If we take the term translated as 'elements' usually, but sometimes 'heavenly bodies', as referring to elements, it would not be referring to elements as we think of them.

"At first glance it might appear that 2 Peter 3:7-13 is describing a literal conflagration of the earth and sky in which the physical elements will literally melt from the heat. The “elements” in these verses which are said in 2 Peter 3:12 to “melt in the heat” are not likely to be the physical elements of the periodic table since the physics and chemistry underlying what makes something a true element had not been discovered yet. Thus the true elements of the periodic table were not called “elements” by the people of that time. When 2 Peter was composed there were only believed to be four elements: earth, water, fire and air."

However, only one of these elements - water - was known to melt (when ice).

"The only possible way in which I can see 2 Peter 3:10-12 being fulfilled in the four known elements of Peter’s day is in the fact that sometimes the orange light from fires can light up the smoke and night air above the flames making it appear as though the sky itself is also on fire. This interesting optical effect can give the illusion that the air, one of the four known elements at that time, is also being consumed by fire."

Having said this, many preterists understand the destruction of the old and creation of new most importantly in covenantal terms, not literal terms (despite there being significant literal destruction in AD 70).

"The Greek word translated elements in these verses is stoichion. Every other time stoichion is used in the New Testament, it refers to the elements or regulations of the Law of Moses.4 Thus these verses may hint at the fulfillment of the Law of Moses predicted in Hebrews 8:13: “By calling this covenant “new,” he has made the first one [the Law of Moses] obsolete; and what is obsolete and outdated will soon disappear.”"

Furthermore,

"the earthly icon or symbol of the Old Covenant was literally burned by fire in A.D. 70 when the Romans destroyed the Temple by burning it with fire. With the Temple destroyed it was no longer possible to practice the Law of Moses. Thus in a way the elements of the Law had truly passed away by literal fire as predicted in 2 Peter 3:12. It should also be noted that Josephus saw the Temple as a symbol or representation of heaven and earth (The Wars of the Jews 3.7). Thus the destruction of the Temple also signified and marked the destruction of heaven and earth."

As mentioned earlier, 2 Peter 3 is working within an apocalyptic Biblical genre (as mentioned above and described in more detail here). As the author goes on to note,

"The prophecies concerning the destruction of heaven and earth are written in an apocalyptic style. Apocalyptic literature is poetry. It is not a strictly literal description of events as one might find in a newspaper. In light of this fact, it is not surprising that the sky and earth did not literally pass away after the Jewish War in the same way that the stars in the sky were not literally “dissolved and the heavens rolled up” at the fall of Edom in the sixth century B.C. as prophesied in Isaiah 34:4-5."

So the description in 2 Peter 3 fits with the events of AD 70 - both literally and covenantally.

Q. In verse 13 we wait for a new heaven and earth wherein righteousness dwells...has that already happened also?

A. Yes. For ex., the article Heaven and Earth Have Already Passed Away says

"The phrase "heavens and earth" is covenantal language. It is not referring to the physical heavens and earth. The Old Heavens and Earth was the Old Covenant and the New Heavens and Earth is the New Covenant where righteousness dwells. Christians are the New Creation and the New Heavens and Earth. Once again, the concept is spiritual/covenantal, not physical/literal."