In my TL the Visigothi and Ostrogothi are ruled by one king but were seperated before. Both "factions" want as much power as possible and want that the king stays close to them.
Which factions? Ostrogothi and Visigothi?
I'm not sure that you'll have that of a distinction between them even if they were separated before (of course, all depend how long they were separated, and how recently they united themselves).
But linguistically, religiously (admittedly they are arian IYTL), culturally they are more prone to stay united no?
Now, maybe you're talking about gothic families against others. It would be more efficient, but it would turn quickly to the ones making alliance (up to matrimonial or not) with roman families (especially the "lesser" germanic families) and the more "pro-germanic".
The Osthrogothi are concentrated around Arelate and hold only a small part of Italy and the Visigothi have the OTL regions around Tolosa. Northern Hispania is Gothic land but not considered "coreland".
What do you mean? Ostrogothic Kingdom is only made of Provence, or you talk only about the place they settled?
If it's the latter, I'm not really sure what you mean by core then : while you have places the goths settled
apparently more than others, they were still surrounded there by a roman majority.
Like the Franks, the core is more likely to be the source of power : palaces, economically powerful region, etc.
For Italy it would be likely central peninsula, for Spain...well, that depends, probably if united with Italy the region of Narbo-Tolosa indeed.
My idea is that the king who has several sons doesn't want that they kill eachother after his death (like otl) so he divides the kingdom: every son must get a part of the Visigothic and the Ostrogothic land and a part of hispania (to prevent a split of the kingdom on "ethnical" lines), one of them is choosen as king over the others.
Which ethnical lines?
I mean, romans population don't began to distinguish themselves before the VII century and were really distinc only ca. mid-IX/early-X centuries.
If it's for the Goths, I don't think they would be that different from each other
For the division of the kingdom, it looks like a mix of roman use of making a testimony will but in this case (as it's still really early in time) it would mean that the division of the kingdom would be permanent and without the germanic principe of communautary unity.
I'm not sure it would be feasable in southern Romania, and have a that early mix between germanic and roman customs (when the rule is more having each communauty having his proper law).
Is that in any way realistic? The Goths rule the land for around 30 years now, it is around 435/440AD.
I think it's too early for having a divied then. It's defenitly too recent to have incidence on settlements and to the reinforcment of royal power.
That said, as noted by Bee, a good solution would be to grant sub-kingdoms (like the frankish unterköningtums, or the sub-kingdoms submitted to bretwalda king in England). But you'll need a bit of time before settling this.
That said, they could be used only for "recognized" lands, and not for more or less arbitrary divisions. In this case Spain, Provence, Dalmatia, etc. Furthermore, they are more likely to be used to control troublesome population (here, rather the place with the less german presence by exemple) for two reasons : 1) military and political. 2)It would prevent the sub-kings to rely too much on a germanic nobility whom the king with "imperium" would want to monopolise. If not the sub-king would have possibility to challenge him.
These sub-kingdoms, that said, even if most probably granted to family (brothers, cousins in first place) wouldn't be meant to be independent of the "original" kingdom but more like marches, while the division of a kingdom "frankish way" doesn't make a kingdom prevalant upon others.