The first example is the easiest to interpret. Parents are often frustrated with the challenge of bringing up children, and they are often heard wishing it otherwise. In that context, 'wishing away today' means wishing that the time of (the day of) raising children would be over. The advice is 'don't wish it away' (don't want it to be over, enjoy it while it lasts, since it'll over all too soon).
We have to guess at the meaning of the second example. I think 'wish away' here might be sort of like the genie in the bottle saying, "I am at your service. Anything you desire I will grant. Your wish is my command. So wish away.' (Meaning: make all the wishes you want.)
The meaning in the third example is also not self-evident to me , because the word 'broadminded' doesn't seem right. Wishing away your fate is something you might do when you don't like what you see as your future. For instance, if you are told you have inoperable lung cancer and are expected to die in three months, you might [mentally] get rid of the threat by wishing it away (simply wanting and believing it not to be true).
Of course wishing something to be true or to come true does not guarantee that it is true or that it will happen.