To what extent were the Warsaw Pact nations puppets of the USSR? To what extent could say, East Germany reasonably stand up to Soviet intervention in their affairs?

I will try to answer your question, but I want to add the disclaimer here that ultimately, it depends on what you consider "a puppet".

I also need to add that the historiography on the Warsaw Pact has seen some important revisions in recent years. The question you ask is also a very complex and large one, so I will limit myself to some significant high- and low- points in the history of WP-Soviet affairs.

First of all, for long, Western historians have not taken the Warsaw Pact very seriously, assuming it to be a monolithic bloc and an instrument of Soviet foreign policy. As a result, few historians found it worth their time to study the relations between the USSR and the Non-Soviet Warsaw Pact (NSWP) members.

As the Warsaw Pact archives have opened up since the 1990s, this image has slowly been eroding as the Warsaw Pact showed significant internal disagreements. In 2015, a groundbreaking study was published based on archival research in Eastern Europe on the relations between the USSR and the rest of the WP. The author, who happened to be my professor in Cold War History, demonstrates how between 1960 and 1975 the Warsaw Pact members "emancipated" themselves from Soviet control and carved out spheres of autonomous action for themselves.

Initially, the 1955 WP Treaty had the purpose of consolidating Soviet control over Eastern Europe. It must be stressed here that this wasn't a one-way street. Eastern European regimes also used and exploited the Soviet Union, as local despots courted favor from the Kremlin to crush political rivals and assert themselves as mini-Stalins or mini-Khrushchevs.

Shortly after the WP was founded, the first crisis broke out in the wake of De-Stalinization. In Poland, the old Stalinist leader Bierut died in 1956 as well, and while Moscow wanted Ochab to succeed him, the Polish Central Committee blatantly threw Moscow's option out of the window and elected Gomulka as their new leader.

In Hungary, the local mini-Stalin resisted the Kremlin's De-Stalinization, and the population revolted, making them beg for a Soviet invasion to suppress it. This further consolidated the image in the West of the WP being mere Soviet puppets.

The Berlin Crisis from 1958-1961 was yet another test for Soviet-WP relations. The WP countries were increasingly dismayed by Khrushchev's erratic foreign policy, while East-Germany was anxious to stabilize its borders. Above all, they wanted to quell the uncontrollable exodus of refugees fleeing to West-Berlin. It was the East-German government that pressured the Soviet leaders to approve and facilitate the construction of the Berlin Wall.

In the meantime, the Sino-Soviet split was seized upon by Albania to head for the exit from the WP. In Romania, where the Split had actually taken place during a Communist Congress where Khrushchev lashed out against Mao in front of Chinese diplomats, the Split was seized upon by the Romanian government to reposition itself as well. They began to complain to Moscow about recruiting agents on its soil, but later on the increasingly nationalistic course led to strong disagreements with the USSR over the status of the Moldavian SSR. Romania claimed Moldavia was part of Romanian history and culture, while the Soviet Union pretended Moldavians for a separate nationality and culture. Romania and Moldavia carried out a propaganda war against eachother throughout their existence. By the 1980's, Romania was only in name a member of the Warsaw Pact but pursued its own foreign policy.

From 1966 onwards, the non-Soviet WP countries took even the initiative in the Cold War. They formulated a proposal for a new European security framework to ease tensions (Bucharest Declaration). By 1969, the proposal was taken seriously enough that it led to official negotiations between NATO and the WP, culminating in the 1975 Helsinki Agreements that facilitated travel and trade between East- and Western Europe, further enhancing the relative economic autonomy from the USSR.

Before that however, the 1968 Invasion of Czechoslovakia marked an all-time low, even for the USSR. Czechoslovakia had resisted reforms until well into 1965. Calls for reform began to emerge and in early 1968, a reformist (Dubcek) was elected to power. Carried away by popular support and a naive faith that he could "repair" Communism, Dubcek practically abolished censorship, released prisoners, promised free elections, and planned to leave the WP and become a "bridge" between East and West, communism and democracy.

The WP was divided on what to do. Particularly East-Germany felt threatened by these heresies so close to their borders, and they pressured Soviet leader Brezhnev to end this "counterrevolution". Phone records show how, on the eve of the invasion, Brezhnev almost begged Dubcek to show he was in control of the situation so he wouldn't have to intervene. It was too late however, and the Soviet tanks invaded along with several other countries. Not all WP countries agreed with it however, and refused to participate in this comradely act of Socialist solidarity.

By then, the Soviet Union more or less declared it a policy, the Brezhnev doctrine, that it would intervene anywhere a Communist regime was in need of some solidarity. That policy died a quiet death in 1981 however, as a movement - ironically named Solidarity- in Poland shut the country down with massive strikes in demand for reforms. The Soviet Union amassed its troops on the Polish border, but with the knowledge of today we now know it was pure bluff. There were no plans or intentions to invade: in fact the Kremlin was already preparing for the scenario that Poland would collapse and leave the WP.

The intimidation worked however, and a Polish general crushed the revolt and established himself as Poland's strong leader.

In the later 1980's the Warsaw Pact countries began to realize they had little to fear anymore from Gorbachev's Soviet Union. From 1987-1988 he began to pull out Soviet troops from Eastern Europe, and make friends in Europe with Thatcher and West-German Chancellor Kohl. In the meantime, local despots in East-Germany, Bulgaria and Romania didn't like it one bit and refused to liberalize. In Hungary however, experiments with free elections resulted in an unexpected defeat for the Communists, resulting in a negotiated capitulation and their unilateral opening of the Iron Curtain.

Masses of Czechs and east-Germans fled to the West through Hungary. Sensing that they had lost their grip on events, the East-German regime fired its hardline leaders and replaced them with reformers, but it was too little and too late. Under pressure of mass demonstrations, they panicked and promised immediate freedom of travel, which led to the opening of the Berlin Wall. Two weeks later, mass protests in Czechoslovakia led to a negotiated surrender of the Czechoslovak Communist regime.

In Romania, the leaders tried to defy the tide of history. The military eventually turned against them and had them executed. Fearing the same fate, the Bulgarian leaders quickly promised free elections. By 1990, the Soviet Union itself was struggling for survival as the Baltics, Ukraine and some Caucasian republics were asserting their independence.

So in short, what I have tried to show is that throughout its existence, the Warsaw Pact involved both coercion and defiance. Recent historiographic trends show that WP states succeeded to pursue their own interests, sometimes by cooperating, and sometimes by defying the Soviet Union. There were limits however. If the Communist systems themselves seemed under threat, it could have bloody consequences. The WP states were also incredibly dependent on the USSR militarily and economically. Whether that makes them puppets, I leave to everyone's personal opinion. The relations between the USSR and the WP countries varied from time to time, issue to issue, and country to country.