I did a search using Google's Ngram Viewer to see how common those three phrases are in written sources.
As you can see, in my opinion has been the most popular phrase throughout the past two centuries. In my view has been catching up lately, but in my own personal experience (AmE) I have not heard it used very often. I would personally always choose in my opinion.
As for to my mind I could not find a SINGLE instance of that phrased used in the way you describe. Every instance cited in the ngram is actually used in a totally different way. For example:
...the terms of which made it clear to my mind that he had not taken No for an answer...
I would wager the reason the definitions you found are so poor because it is a very uncommon phrase.
As for the difference between in my opinion and in my view I would agree with Global Charm. In my opinion allows one to stress the my to emphasize what your opinion is in contrast to someone else's opinion. Or you can stress the opinion to stress that this is just an opinion and not a fact. In my view only allows for the emphasis being placed on my.
In addition, a popular phrase used across various forms of media is IMHO (in my humble opinion). This phrase has picked up a bit of a snarky, rude connotation in some cases. You can read more about that here on another question. So that can add an additional subtle layer of feeling when you use that phrase on the internet or with younger people.
To keep it short and sweet: generally speaking, I personally see in my opinion and in my view as synonyms. But as previously stated, in my opinion is more common.
If you want to do more research, many others have already asked this question across various websites. Perhaps you would be interesting in reading them.
In my view, in my opinion, in my point of view (wordreference.com)
In my opinion, From my point of view, In my mind (wordreference.com)
“I think …” or “In my opinion…” or “From my point of view…” (ELU Stack Exchange)
'According To Me' Or 'In My Point Of View' (englishforums.com)