Bitting

Question
I have two red-ear turtles and the lager turtle is bitting and shoving the smaller turtle just to get its space.

Answer
This is usually a sign that the tank is too small. Aim for about 10 gallons of water per inch of total shell length.

If the tank is big enough (and they usually are not), then the  bigger turtle may just be a bully. This is fairly common in Red-ear Sliders.

http://www.redearslider.com