Yes, I'm playing KR now, sorry if I didn't tell it!
But it's not a problem of an event, this war was only after my initiative: it's a problem of the game itself, I don't know if that can be changed.
The rules are:
1) doesn't matter which armies are present, if an attack starts from the province of country A, then the owner of new provinces is country A;
2) however if country A is puppet of country B, then the province goes to country B, unless country A has a core in that province (can't remember what happens if both A and B have a core on a province that A occupies);
If you make an amphibious landing starting from your province, then naturally you would gain control of the occupied province. From this province, under your control, you can land your armies and start occupying the rest of the country. So you would only need 1 amph landing and then lots of naval transport.
There is also the possibility of making claims and then if your ally doesn't have core/claims there and your relations are very good, then they will probably give you the provinces (over a certain period of time, it's not immediate).
However in this case, in KR there's probably an event that forces the re-creation of Carlist Spain, before they can give the provinces to you. This is why I said that you can either modify this event or make your own event to change the situation.
EDIT: Czaristan was faster than me and he is right too.