Sandra,
I've listened to your sample 4 times now. And it's so obvious that you can carry a tune, so that's good -- but don't fear that your voice lacks a certain "perfection" of sorts.
You might just need to embrace the "Übung macht den Meister" concept when it comes to honing your voice, and the impression you want to make, vocal coach or not.
I retrieved some youtube examples of female singers who you might want to listen to.
(I hope this is okay with the rules & regs?)
Karen Carpenter's lone-ish vocal for "Masquerade"
https://www.youtube.com/watch?v=lKy77tpT_doThe full album version:
https://www.youtube.com/watch?v=ljWyIKyua8cFiona Apple, Extraordinary machine recorded
https://www.youtube.com/watch?v=T14ux2k7rk0Fiona singing it live:
https://www.youtube.com/watch?v=YsMZkCLxfkM&feature=relatedPhoebe Snow singing Harpo's Blues
https://www.youtube.com/watch?v=0SESmndcKI0Janis Ian has a higher register than you, but this might be illustrative:
https://www.youtube.com/watch?v=VMUz2TNMvL0&feature=relatedBasia sings higher & lower, instructive vocals
https://www.youtube.com/watch?v=sMmY70RPI24Tracy Chapman sings Fast Car live
https://www.youtube.com/watch?v=Orv_F2HV4gkNorah Jones' Cold Cold Heart, live
https://www.youtube.com/watch?v=g35zS1tVO3o... and Come Away with Me
https://www.youtube.com/watch?v=c1V5Wk9gb4U These female singers may not represent your style, but hearing their takes on those tunes might offer something in the way of practice.
Cheers,
Christa