I understand why you don't want her to loose her heritage, and please please please don't dismiss the devestating effect losing her father will have on her at such a young age. Two years is NOTHING, i say this as an adult who lost her father 8 years ago. It still hurts like hell.
The thing is, if you continue to force the spanish on her then you are going to end up with her not wanting to embrace it and rejecting it. She skypes her relatives, visits and you speak spanish to her (albeit not grammatically perfect, so what, is your english perfect? I know mine isn't).
Maybe she finds it weird having to stay in the room on her own with the tutor, especially if you are in the house and i say again, the tutor clearly isn't engaging her.
Don't try and over compensate for her, and your loss by trying to raise a perfect child - you are way to strict, she is five years old. Yes there are consequences but what you are doing is too much. Just let her BE and learn and develop. You speaak so proudly of her - give yourself credit for that. She sounds like a lovely little girl.
I have a friend who constantly battles with her DD, aged 8, punishments for stuff that me and DD would have a giggle over - her DD is pretty troubled actually. Its sad to watch - all for what? A perfectly behaved automaton?