Seeking guidance alone, I only really want one thing

Just for context i was born a muslim, that alone is a blessing. But overtime I have really struggled with my faith. Even as soon as I could talk I always questioned things I don't understand. One of my first memories is me asking allah if he really exists and I don't know why.

Overtime, I began struggling with my mental health for multiple reasons which only distanced me away from faith however, I never hated islam or being muslim. I never did any zina, and I never really committed any big sins even though at some points I never identified as muslim. However, over the past few years i've noticed the gaps of happiness between me and other muslims around me. Between me and my sister- who's so much more faithful than I am. Between me and my neighbors and other classmates. Between me and muslim influencers I follow who are living my dreams.

I am dedicated currently to getting back on my deen. I want to be happy like everyone else. I want to fix my relationship with my mother and siblings. However it has been hard for me.

There's only one thing I really want out of life. I want to study abroad in korea for one summer. One month.

I've always dreamed of it and I've dedicated years of my life to fluency in korean. I study it harder than anything else and it's the only thing I work on in my free time. I always so immensely jealous of my cousins who got to experience studying abroad or my neighbor's daughter who got to visit australia on a school trip as well.

As soon as I got back into praying it is truly the only thing I ask for with all my heart. I've wanted it for over a decade and I've never asked my parents for anything else. I cry when I pray for it and even as I type this. I plan to pray tajjahud every night for it starting today.

My question is how can I make proper Dua for this? how can I properly pray tajjahud? more importantly how can I properly ask my mother for it? i've truly never rebelled once in my life and i've never even attempted to defy my parents

It's a simple month long study camp for korean and nothing else. I won't be doing anything else over there and i've never had the interest in anything haram at all.

please help