Im booking progression, I managed to play the first 2 chords almost perfectly like the song,
but still stuck on the third chord...
It's a slow process, but if you are satisfied with the way you are playing the Dm and the C then you are definitely making progress.
I would say that ALL guitar players struggle with the double-barre shape needed to play the Bb, because in order to nail it "perfectly", it requires a bunch of things to happen simultaneously, all of which take practice:
> strong "clamping" muscles (which takes a while to obtain),
> the top joint of your ring finger to bend in an unnatural way to be able to cleanly fret the D, G and B strings while simultaneously staying clear of the high e (so that you don't mute it), and
> touching the low E with the tip of your index finger to mute it.
One tip for you on the Bb: Don't worry about the high e. Many players find that they are satisfied if they can play it as x1333x, with the high e muted by the middle joint of your ring finger. You may find that the sound is OK for you with the high e muted. Like I said, a lot of players are.
I've been working on that shape for a couple of years and still manage to hit it only about half the time. The good news is once you get good with it, you probably realized that it can be moved all the way up the fretboard (slide up 2 frets for C, slide up 2 more for D, etc.).
Anyway, try that open chord progression (starting with Em) and it will help you work on the strumming. And again, if you tune down two half-steps, you'll be in tune with the record, but you'll notice that there is something not "quite" right about the sound. That's because the chords are the same, but the chord VOICING is a bit different. Once you get the strum down, tune back up and work on the chords.
Good luck. Keep me posted.