[disclaimer] What I am going to say here applies to the verb desavenir(se) as it is used in Spain. It may well be that it is used differently in Latin America, and in that case those of you who know/have learnt Latin American Spanish probably know more than I do about it. [/disclaimer]

The verb desavenir(se) is both pronominal (i.e. has to have personal pronouns attached to it to complete its meaning), and reciprocal (the action is done and received by the different agents simultaneously). So, if Faldage says "Inselpeter y yo tenemos que desavenirnos", he's saying that he and Inselpeter have to disagree (or fall out) with each other, not with a third party. Let's hope this doesn't happen.

If Inselpeter and Faldage as a pair want to disagree with someone else, some good verbs are discrepar and disentir. Bringing the post back to topic, in Spanish we can use use both forms tener que and haber de (derived from Latin tenere and habere), to express "have to". So, Faldage has several stylistic options to pick from:

"Inselpeter y yo tenemos que discrepar" OR "Inselpeter y yo hemos de discrepar"
"Inselpeter y yo tenemos que disentir" OR "Inselpeter y yo hemos de disentir"

Sorry for the ramble.