*I assume you know the basic maths stuff concerning angles, movement, distance and all the other stuff.*

You have these goals:

 - reach destination
 - do random stuff
 - stay inside (rectangular?) area of playfield

Your plane could have these properties:

 - position `pos`
 - forward-speed `vel`
 - forward-acceleration `acc`
 - heading/rotation in degrees `rot`
 - angular velocity (rotation per second) `rotVel`
 - angular acceleration (change of rotation per second) `rotAcc`

Of which `pos`, `vel` and `rot` are chosen when spawning the plane and then **never touched again by the random movement code** and the others are used to steer it (randomly) towards it's target.

To move the plane, this is getting executed each tick (delta is the time between two updates):

 vel += acc*delta;
 pos += vel*unitVectorOfAngle(rot)*delta;
 rotVel += rotAcc*delta;
 rot += rotVel*delta;


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So what you could do with this:

**1. Loops and turns**

You set `rotAcc` to a random positive or negative value, and leave it like that until you reach a randomly chosen Angle (*or for a randomly chosen time or until you are heading towards a randomly chosen point, whatever works best*) and then set `rotAcc = -rotAcc` to smoothly decrease your turnrate until `rotVel` is zero again. In the image, two example-paths are shown, red is the acceleration phase, green the deceleration phase.

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[![loops and turns][1]][1]
 [1]: https://i.sstatic.net/L1QQW.png


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**2. Gliding back and forth**

You set `acc` to a relatively big negative value and decelerate until you move back fast enough. Then you wait for a random amount of time and set `acc` to a high positive value until you reach your original speed again, then set it to zero.


**3. Reaching your destination**

You should constrain the randomness of your planes movement based on the time that has elapsed since it was started and the distance to your goal. just initiate the random moves less frequently and try to correct its path towards the target, by tweaking `rotAcc`.

**4. Constraining the fly area**

For countering situations in which the plane goes to near to a border, you could use a combination of gliding back and doing a fast loop or a manual turn.

**5. Mix it up and time it**

I can't help you there, you will need to figure out all the tweaking and timing out for yourself.