Given that the two brothers are never on stage together, what we know about their relationship comes from what they say to others and what others say about them.
We first hear about Frederick and Senior from Charles. Charles reports to Oliver that Duke Frederick has usurped his brother Duke Senior. Senior is now exiled in the forest with a group of friends. His daughter, Rosalind, is allowed to remain at court with Frederick's daughter, Celia.
However, in scene 3 of act 1, Frederick has an outburst and changes his mind. It seems his grudge does extend to his niece, and Rosalind must leave. In act 2, scene 2, he is angry to learn that Rosalind and Celia have sneaked out with no one noticing. Thinking they might be with Orlando, he insists that Oliver find his younger brother. Through Frederick's outbursts, we can see his intense dislike for his brother, although this dislike does not seem to be justified.
Meanwhile, in the forest, Duke Senior adapts well to life away from court:
Now, my co-mates and brothers in exile,
Hath not old custom made this life more sweet
Than that of painted pomp? Are not these woods
More free from peril than the envious court?
He does not express the same level of hatred that his brother does, even though as readers we might believe he has more cause for hatred.
It is interesting to note that Frederick and Senior are not the only brothers in the play. Their relationship can be compared to Oliver and Orlando, who similarly start the play with problems but make peace in the end. Perhaps we don't need to see any interactions between the Dukes, because we can look to Oliver and Orlando instead.
The play begins with another character reporting on Duke Frederick's actions, and it ends similarly:
Duke Frederick, learning how that every day
Men of great worth resorted to this forest,
Addressed a mighty power, which were on foot,
In his own conduct purposely to take
His brother here, and put him to the sword.
And to the skirts of this wild wood he came
Where, meeting with an old religious man,
After some question with him was converted
Both from his enterprise and from the world,
His crown bequeathing to his banished brother,
And all their lands restored to them again
That were with him exiled.
Jaques tells us that Frederick has turned to religion and now sees the error in his ways. Duke Senior does not seek any revenge, and we are left to assume that all is well between the brothers. We should also remember that Jaques is Oliver and Orlando's middle brother, and he gives this news during their wedding celebrations. Jaques decides to live in a monastery like Frederick, which again suggests some parallel between the different brothers in the play.