How to smooth out points

Hendy,

In addition to what has already been said, it is generally better to see the whole appearance while you create it.

For a simple one to two mirroring with a vertical axis as the one in question (before rotating it, and before expanding it), you may see the reflexion live after each Anchor Point if you start out as follows for each stroked path (presuming your creating the left side), Smart Guides being your friends:

1) Create a vertical path of sufficient length to serve as the axis; you can just Click twice with the Pen Tool, letting Smart Guides guide you;

2) With the Pen Tool ShiftClickDrag to the left from somewhere on the line from 1) to create the first (centre) Anchor Point of your path and going left, thereby making sure you get a smooth point;

3) ClickDrag (or just Click) a (rough) sketch of you second Anchor Point from the assumed position;
4) Apply Effect>Distort&Transform>Transform>ReflectX with 1 copy and the middle right side Reference Point chosen;
5) ClickDrag (or Click) anew from the second Anchor Point for real and go on, ending by ShiftClickDragging on the vertical line from 1), thereby making sure you get a smooth point here too;

6) Object>Expand Appearance and Ctrl/Cmd+J to join the two halves into a closed symmetrical path.

Ctrl/Cmd+Z Undo is your friend: you can just go back and redo while drawing the basic path.

But you can have a look at the MadPattern templates,
http://madpattern.com/

Or you can have a look at the MirrorMe plugin from Astute Graphics,
http://www.astutegraphics.com/software/mirrorme/

Try trackpad tool.

The strokes are outlined, which makes this even more difficult. 

Maybe starting from scrtch is easier and faster. WHen drawing this, draw it exactly horizontal. Make sure when you set the anchors at the mirror axis that their handles are exactly horizontal.