What were Shakespeare's views on parenting?Want to understand what he felt about the way parents were, or what he felt they should do, or what they...

This is hard to really say, because it is not always apparent as to which things the characters do are things that Shakespeare himself agrees with and which things are not.

I want to focus here on the Capulets -- Juliet's parents.  Early in the play, when things are still good and everyone seems pretty happy, the Capulets are not too demanding.  They are willing to let their daughter postpone marriage if she wants and are, in general, seemingly interested in what she thinks.

Later in the play they are really quite abusive when she does not want to marry Paris right away.  Lord Capulet, especially, is very violent in his language.

So which did Shakespeare approve of?  I think he approved of the earlier attitude, putting it, as he did, farther from the tragic ending.

I suppose you can see a similar thing going on when he does not let Egeus get his way in "A Midsummer Night's Dream."  So perhaps you can argue based on these two plays that Shakespeare thought parents should take their children's wishes into account.