Should the ties of kinship be limited to only the father with his brothers who are religiously negligent and prevent their children from him, or what do you advise?

If you fear the corruption of your children, you may prevent them from visiting their paternal uncles to the extent that removes the harm, and you suffice with visiting them yourself. Utilize the visit to offer them sincere advice with wisdom, especially the uncle with destructive ideas. If they are guided, then praise be to Allah. Otherwise, you may boycott the one among them whom you hope will benefit from the boycott.