Rose didn’t care about the traveling. Rose stayed on the TARDIS to stay with the Doctor. When Rose was trapped in that parallel world she wasn’t missing the running and new worlds, she was missing the person she was in love with.
When she finds him again, and when he leaves as she’s kissing tentoo, that wasn’t the Doctor choosing for her. She could have easily walked on that TARDIS and he would have left with her. When she asked them both the last thing he’d said to her, and what he’d been about to say before fading, that was Rose making her choice.
There were two lives in front of her. She could go with the Doctor, and it’d be the same as before. Or she could stay, and finally be loved by him in the way that they both deserve.
So she kisses him, and she chooses to stay. When she’s pressing his lips to hers, she’s showing the other Doctor that things are going to work out the way he wants them to for her. If she would have just told him, there’d always be that doubt in his mind, but she showed him. When she kissed the other Doctor she was telling him in the most concrete way that she would be honored to be loved by him and that she’d much rather have that than traveling.
People always get mad that Rose had no choice, and she would have rather gone with the Timelord Doctor, but they don’t see that this time that wasn’t true. He wanted her to be happy. He needed to give her up because he knew that she’d be so much happier if he would be able to love her back, but he didn’t force anything on her. He stood in front of her and he told her he’d never be able to say it, but there was a version of him that could. That she had a choice, finally, in whether she would go or stay.
And because she loved him so much, and so desperately, and so completely, and because she knew she’d never have another chance to be with him in this way ever again, she stays.