Could the Court order that access to the Proposed Ward be permitted for all family members? Sure. Even the Court might recognize, however, that unsupervised access is not in the Proposed Ward's best interests, and those best interests are the Court's chief concern.
It sounds like you're in the early stages of a disputed guardianship case. If you think that tensions are running hot now, wait until the Court is asked to approve attorneys' fees from the Proposed Ward's Estate. These fights are emotionally and financially draining, and you'd do well to speak with your own attorney to learn what rights and options you may have to assist the Proposed Ward.
I see that you're posting this question from Fort Worth. Our attorneys frequently practice in the Tarrant County probate courts, and I'd be happy to visit with you in more detail if you'd like.
This answer does not constitute legal advice. I am admitted to practice law in the State of Texas only, and make no attempt to opine on matters of law that are not relevant to Texas. This answer is based on general principles of law that may or may not relate to your specific situation, and is for promotional purposes only. You should never rely on this answer alone and nothing in these communications creates an attorney-client relationship.