Yes there is wonderful story of Hanuman fighting with Lord Shiva and Shree Rama only appearing in the battlefield but not fighting with Shiva.The story is from the time of Shree Rama's Ashwamedha Yagna.
Rishi Agastya advices Shree Rama to perform Ashwamedha yajna. Shree Rama then appoints Shatrughna as protector of sacrificial horse and the horse is set loose. During the time lots of times the horse gets caught and relieved . Once the horse enters into city of a king called Veeramani who was great devotee of Lord Shiva .And his son seize the horse. Battle takes place between Shri Rama's army ,who was appointed to protect the horse i.e. Sugriva , Puskala (son of Bharata ) etc. In that and Lord Hanuman appears at battle to protect Rama's army and to free the horse as a devotee , Lord Shiva too in order to protect his devotee (Veeramani) for the boon appears and fought with each other
Puskala gets killed killed in that battle by the hand of Veerbhadra and later gets revived by Hanuman by sanjeevani buti.
The very detail story and its Narration is found in Padma Purana - Volume 5 - Section 5 -Patal Kanda. The whole Patalkanda setion is this big story about Shree Rama's Ashwamedha horse and fight between Lord Shiva , ganas and Shatrughna and , Lord Rama's army.
On the twelfth day of the war Shatrughna fired the Brahmastra at shiva. Knowing this Lord Shiva in response discharged Bramasiras at Shatrughana and Shatrughna became unconscious. Shiva attendants knock-down many of heros of army like subahu ,sumada and Puskala. Hanuman saw that these servants of Lord Rama are helpless and wounded. He rushed to battleground to fight with Lord Shiva.
Fight Between Lord Shiva And Hanuman. -
Chapter 44 - Hanumat on the Drona Mountain
Hanuman breaking chariot of Lord Shiva
1 The hero Hanumat desirous of killing the lord of gods , came near Rudra on the battlefield and (said to him) :
2-5 O Rudra , what you are doing is against religious merit. Therefore , I desire to punish you eager to kill Rama's devotee. My brave (hero) Puskala is killed and Satrughna also has become unconscious . Therefore ,I shall know you , ready to destroy three worlds , down o Sarva ( i.e.Shiva) , you who are averse to Rama's devotion , stand carefully.
10-16 When lord of Nandi was speaking like this , Hanumat extremely angry took a big stone at hit it at his chariot. His chariot , hit with the stone was broken to pieces along with the charioteer , horse ,flags and banners. Seeing Shri Shiva without chariot Nandin ran to him. He said to the great god Sit on by back ." Hanumat was extremely angry with Shiva , who was seated on the back of the bull. **Hit with it the lord of the beings (i.e. Shiva ) took a sharp bright ,spear , having three points and resembling the flames of fire .
Seeing that great trident bright like fire came to him (i.e.Hanumat)
took it in his hand and in a moment quickly broke it into ( pieces as
small as sesamum seeds).
Lord Shiva firing his missile "Shakti" at Hanuman.
17-21 When the lord of the Monkeys quickly in a moment broke the
trident , Shiva took in his hand the (missile called ) Shakiti
entirely made of iron . That Shakti discharged by Shiva stuck to (i.e.
hit) the chest of intelligent (Hanumat) (and) in a moment the lord of
the monkeys became affected.
Hanuman hitting a tree on Lord Shiva's chest.
17-21 In a moment having overcome that pain he seized a strong tree and hit it with Shiva's chest adorned by great serpents. Shiva seeing the tree discharged by (Hanumat) and hitting his chest got angry and took a terrible pestle in both his hands.
After fight of Lord Shiva and Hanuman Lord Shiva gives boon to Hanuman. And tells him to go to Drona mountain to revive wounded and dead.
Fight between Lord Shiva and Hanuman stops and Lord Shiva giving boon to Hanuman.
29b-32 He said to the lord of monkeys who made him every moment very much disquieted " O follower of protector of Raghu's , you are blessed . You have today done a great feet , so that i am very pleased with you. You having a great speed . I am no easily obtainable by means of charity or sacrifice or a little penance. Therefor ask a boon from me.
Then Hanuman revives the dead and wounded by bringing the Drona Mountain ,during which he fights with Indra and all gods.
Chapter 45 - Shree Rama appeared at Battle scene when remembered by Shatrughna.
52b- 60 When he was speaking like this , Rama who was dark like the blue lotus ,who's eyes were having (tucked) a deer's horn to his waist, and who had the body (i.e. like that of ) an initiated person , was seen on battlefield . Seeing him on battlefield Shatrughna was amazed.
After Shree Ramas arrival both he and Lord Shiva discusses about the happening and Lord Shiva tells Rama that he wounded Rama's army and protected veeramani only to maintain truthfulness. And he himself given the boon to virmani when he did penance in the Mahakali temple of Ujjayini, that "i shall dwell for your protection in your city till Rama's sacrificial horse come to you " so i was keeping the words.I am now returning your horse .Then Shree Rama also says that there is no difference between us.
Discussion Between Lord Shiva And Lord Rama and returning of theSacrificial horse to Rama.
19-22 It is but the duty of gods to protect their devotees
.You have done auspicious deed ,since you have now protected your devotee .O Shiva you are in my heart (and) I am in your heart .there is no distinction between us (only) the wicked minded fools see (the distinction i.e. they look upon us to be different .those who are your devotees were (i.e. are) my devotees only and my devotees also salute you with great devotion.
This is the happy ending of the story. Now the question arises how Hanuman and Lord Shiva fought each other? No It was just (Shiva protecting his devotee)Maya of Shiva and Rama to show the world that gods are bound to protect his devotees and devotees are bound to the lotus feet of gods(Hanuman true devotee of Rama). Lord shiva was just testing Hanuman for his devotion.
This is amazing story , besides of above the whole purpose of this wonderful narration is tell us that "there is no difference between Lord Shiva ,Lord Rama or any between any other god. And their devotees should not consider then separate and now my most favorite. Story.