Should I still be paying child support if my ex-wife and her new husband have a much better standard of living?

You can apply for a modification of the child support award, under the theory that since your ex-wife is now supported by a new husband, her individual living expenses have decreased, and therefore her ability to provide support has increased. You may be able to get a downward modification, but it is extremely unlikely that your duty to pay child support would entirely disappear.

For example:
Your ex-wife moved into her new husband’s home, and she no longer pays for her rent and utilities each month. Since she no longer has this expense, she has more available income each month, which could be contributed towards the support of the child(ren).