HLTA Questions

Hello! My first deployment is coming up to Latvia. For HLTA, I want to meet up with my wife to an alternate location in the middle of my leave. For the first half, I am planning to just go around Europe. Am I able to just fly out of Latvia to somewhere in Europe at my own expense and let PSP book a flight to an alternate location (around $1500) and back to Latvia?

Example,

Riga to Italy - Own expense | Italy to Japan, Japan to Latvia - PSP