Is it covalent or coordinate covalent bond ? Because it can be a bond between O and 2 H atoms and so it will be covalent bond . And it can be a bond between H (+ve) ion and Oh(-ve)ion and it will be coordinate covalent bond ? If covalent ,why not coordinate covalent ? ,and if coordinate covalent why not covalent??
The water molecule is symmetrical. The two bonds in it are the same and cannot be distinguished. It makes little sense to label them as different types of bond.
Since the bonds are symmetric, the electron distributions will be the same. We can't tell, nor do we care, where the electrons "came from" and all we can tell is that electrons are shared between hydrogen and oxygen to create the bonds.
So the distinction between covalent and coordinate-covalent is irrelevant for the water molecules and does not help us understand anything about it.
Perhaps it helps.
Let's take two hydrogen and one oxygen atoms. They come together and react to form water by covalent bonds involving their valence electrons. Fine.
Now let us take a proton and an OH- ion. The ion will "datively" share is lone pair to the proton and water is formed. Again fine.
How do you resolve now what O-H bond is what? They are the same type of bond and does not help nor does have sense to make a distinction between them.
It is exactly what you have sketched. But the arrowed bond is not meaningful anymore as for the two electrons are one from O and one from H, nothing can keep track of history here.
Or as said in a comment: no concept on having a dative bond between ions.