Before Adam arrived, Amy did tell Jonah everything she felt and all her reasons in a few small words in the middle of a contraction: it wasn't just sex, she had feelings and stuff but it wasn't fair to put pressure on him with the baby and everything. And Adam is the father, so that same sense of fairness to him and her baby is to let them bond without her dumb ex somehow doing a Bo and thinking having sex with Jonah while pregnant could somehow make him not the dad.
She didn't send Jonah away, but couldn't ask him to stay. But she loved that he was there for her throughout, and how different that was from her ex. They have a journey ahead of them, and as a viewer I've become invested in that.