I don’t know about upbringing exactly; I think probably an education that was similar to hers, a focus on languages (which seemed to be what ended up happening anyway, under Henry’s guidance, so maybe that would have been mutual). Evangelical-leaning tutors; if she could manage to secure some as she was sponsoring several scholars that were evangelical-leaning…perhaps Nicholas Bourbon, had he stayed. Anne and Henry were both composers themselves, so probably an immersive music education as well. And she’d want her to read City of Ladies, and works by Marguerite de Navarre.
She seemed to want a French marriage alliance for her (although that was rebuffed); I think had she had a son by that point, the betrothal of Elizabeth and the dauphin would probably have been secured (although he died in 1536, so…). Had Henry made an alliance with the Emperor; they would both try to secure a betrothal with the future Philip II of Spain.