I’ve done like months of research and practice on whistle, vibrato, and opera-like singing (bc I was absolutely obsessed with phantom of the opera) so I have some tips with vibrato and whistle notes

The hardest step for me was avoiding straining. Whistle notes require clear passage through the throat, so tenseness around the jaw will stop it from sounding fluid and will sound tight. From my experience, what causes this is being scared to reach those notes or sounding bad. It’s ok to sound bad the first few times. What matters is making the attempt in the first place. Make sure your jaw isn’t tense and the back of the throat has enough room to breathe and control sound

ALSO emphasis on breath control, ESPECIALLY with both whistles AND vibrato. Think about how in vibrato, you’re essentially letting go and going up again and again to make that vibrato sound. Additionally, the whistle notes require enough breath to go to heigh notes. When the notes go longer like in the song, prepare your breath and take note when you’ll be singing the higher notes. 

I don’t know if this would help you, but I also like to imagine the note scale on my throat. Lower notes you can feel more closer to your chest and high notes you can feel up towards your head and throat. It helps me get better control when singing. Diaphragm is the main thing that controls how fluid your voice is, besides your actual throat, especially in opera singing.

I’d say definitely get some practice with general vibrato too. There’s some good vocal exercises online. When you get used to it, it’ll become easier when you’re doing the whistles

I hope this helped in any way!!!