In some incidents of Mahabaratha, most of the Pandavas except Bheema reacts less than expected.
Were they submissive? Are there any slokas explicitly saying about the submissive behavior of most of the Pandavas?
NO, Pandava-s were Not submissive.
Mostly the verses are found which are other way around, i.e. praising their heroic nature.
There are no such instance noted, when they heartily acted submissive to their Kaurava cousins, let alone any others.
At times they remained passive due to the observation of Dharma.
They remained passive during Draupadi's insult. During that time, they already had become slaves of Duryodhana by stacking themselves. Hence they were observing the DAsa dharma to their evil [supposed] masters.
At last when Yudhishthira put himself at stake...
Yudhishthira, said--'I alone, the eldest of all my brothers and dear unto them, am still unwon. Won by thee, I will do what he that is won will have to do.'" [Sabha Parva]
Later when Draupadi was also won and was to be insulted. Bhima got angry on his elder brother, but Arjuna pacified him.
"Bhima said, ... I shall burn those hands of thine. Sahadeva, bring some fire.
Arjuna hearing this, said,--'Thou hast never, O Bhimasena, before this uttered such words as these. Assuredly thy high morality (viz. Dharma) hath been destroyed by these cruel foes. Thou shouldst not fulfil the wishes of the enemy. Practise thou the highest morality. Whom doth it behave to transgress his virtuous eldest brother? The king was summoned by the foe, and remembering the usage of the Kshatriyas, he played at dice against his will. That is certainly conducive to our great fame. [Sabha Parva]
This answer discusses, why Yudhishthira had to gamble at first place. Linked with Yudhishthira, all his brothers also remained silent.
There is no submissiveness in following Dharma except to Dharma.
The other such confusion between passive and submissive behaviors may arise during the Kichaka Vadha instance. But it's well known that, PAndava-s didn't want to uncover their identity by killing Kichaka in an explicit combat. Had they done it openly, spies of Duryodhana would have found it easily (which they knew delayed). And Kaurava-s might have trapped PAndava-s for another 12 years in forest.
However, Kichaka was secretly killed anyways for Draupadi's insult.
This Vrikodara is brave and is a hero full of wrath. He is reckless in protecting his body, and in strength of limbs he is superior to all. While leading a life of concealment in the city of Virata, relying then on the might of his bare arms, for doing what was agreeable to Draupadi, he secretly slew Kichaka with all his relatives. [Karna Parva]
Another instance of submissiveness of Arjuna alone appeared during just before the Mahabharata war. However as well all know, he redirected it towards Shri Krishna and after listening to Bhagavad Gita, he threw away the unmanliness and engaged into the great war.
An interesting note on Bheema being reactive. Originally the Mahabharata war was not supported by Bhima either, as discussed in below post:
Who among the Pāṇḍavas supported the main Kurukṣetra war and who didn't? What were their reasons?