Am I obligated to maintain ties with relatives whom I know envy me and wish me ill, or is it permissible for me to reduce my visits to them and suffice with my parents visiting them?

Maintaining kinship ties, especially with paternal and maternal uncles, is an Islamic obligation. You must connect with your paternal and maternal uncles by any means, such as calling, visiting, and giving gifts, in compliance with Allah Almighty's command. There is no need to inform them of all your affairs, especially those you fear they might envy. Your parents' connection does not substitute for your own, unless you genuinely fear harm from them. Mere disliking them or fearing their envy does not negate the obligation to maintain ties with them.