Why is it that if we are sitting in a plane...?

Centripetal force, it's the force that pushes you against your seat because the plane is traveling in an arch. The same thing happens when you swing a bucket of water over your head.

You are exaggerating the turning degree rate. Anyway to answer your question the actual force you experience when a plane is turning is the force between the gravity and the turn rate acceleration of the aircraft. For example picture yourself facing an aircraft on its back, then the aircraft is turning West, this means the passengers are supposed to feel the force going East but because of the earth's gravity you also have a force going South that counteracts the Eastward force generated by the aircraft turning to the West. The Southward force(Gravity) and the Eastward force's(turn) contradiction will mean that the actual force acting on the plane will be at South East. This is more popularly known as the G-Force.

Commercial jets (and pretty much every other plane) roll when they turn. This has the effect of keeping your local 'up' direction aligned with the vector (g - a), where g is gravity and a is the plane's acceleration. In other words, the plane tilts such that the combined effects of gravity and the plane's acceleration always point up, from the passengers' point of view.

It's the same effect as when you ride your bicycle at speeds above 10 mph and make a turn. Your bicycle is inclined towards the inside of your turn - and yet you do not fall and the bicycle does not fall to the inside. If you would force your bicycle to keep straight upright while doing a turn, you would fall towards the outside of the turn. Both, the bicycle and the aircraft have to provide a force towards the inside of the turn to prevent the vehicle from traveling in a straight tangential line due to inertia.

passenger jets will only ever make a routine turn of a maximum of 15 - 20 degrees the angle needed to move objects is a minimum of 35 degrees. when you look out your aircraft window the glass is dual layerd making the effects of refraction drastically magnified... it will make it look like your on a steeper angle than you really are.

Well... I'm not a rocket scientist.