After meeting Yukki's mom, Yuno is glad that she didn't have to use her "tools" to convince her. But at the end we know that this was the second time she went through her life, which means that she already passed by her first meeting with Yukki's mom. Yet she didn't expect to be accepted and therefore brought "tools" along with her....
Does that mean that in the first world she actually forced Yukiteru's mother to accept her in some way?