Ok, as a mom I can help you out here. The seat you need is rear facing which does take up more room than the forward facing.
#1 Move the passanger seat all the way forward.
#2 Set the seat in the rear facing position in the back seat.
#3 Pull the seat belt out all the way(it should click as it retracts back into the housing).
#4 Push down as hard as you can on the car seat and buckle in. There should be no side to side movement.
#5 Move passanger seat to desired location and adjust the back of the seat to desired position. (Note seat will push up on the baby seat the further you have it moved back)
My child's first mustang ride was in a 1997 cobra.
Something you might want to invest in is a carseat mat. This will help keep your leather seats looking nice. They trap food, drinks, and keep the seat from getting cracks, dents, and dimples.
Hope this helps! Best of luck, and congratulations.