What does this mean for relations between the Visigoths and Ostrogoths(Eutharic was a Visigothic Noble. Gothic reunification???

)?
It is too late for the Visigoths at this point, Eutharic died in 522, well after the Franks had displaced the Visigoths from Gaul. You need to either stabilize their succession or have them conquered by the Ostrogoths for this to work. Even then you will still have the instability that comes from an Arian elite ruling a Nicene population that ruined the Visigothic Kingdom.
What happens with the Franks?
Most likely, they make and break alliances as it suits them with the any surviving Ostrogothic kingdom.
What happens when (and if, I suppose) the Byzantines come around?
Depends on the path the Ostrogoths take and how the Nicene population of Italy views their overlords.
Bump. I'm really interested in a surviving Ostrogothic kingdom and would like to know what you all think about this scenario.
I think you need to set the POD a little earlier. Keep the initial Ostrogothic kingdom small -- maybe just the Po Valley. This will help keep the relatively small Ostrogothic population concentrated and allow them to establish themselves. Trying to have them quickly become a renewed Western Empire is bound to fail. It may be useful to import some other Germanics to boost the population. Refugee Gepids or Lombards fleeing Byzantine attacks could help.