am i still entitled to the agreement and half the time with my step-son?
No, step-parents have absolutely no rights or legal standing. It is very unlikely a court would, essentially, give YOU visitation.
. His mother does not have a job and bounces back living with her mom or her dad, so I want to make his environment here stable as possible.
And visits with you would not be "bouncing" the child back and forth? Courts know the greatest stability in a child's life is the primary caregiver, not particularly WHERE she lives. Indeed, the child's bio GP's are usually more important in the child's life than a step-parent; nothing wrong with him living or going there. Being with family IS stability.
A step-parent's job is a thankless one; if you can love the child unconditionally tho without any actual authority over him, you would be enriching his life immeasureably. But when step's get too involved, denigrate the bio-parent's parenting, etc, it only causes issues.
So if you love the child, don't make trouble except in the most dire of circmstances...and be sure to let a lawyer make the decision about "dire" as what average people think the law should address are usually wrong.