Yes, I wouldn't go.
The cousin (and your parents!) seem pretty far gone, in terms of Catholic doctrine and truth.
Losing such (protestant? non-Catholic?) influences will not be a bad thing.
Matthew 19:29
And every one that hath left house, or brethren, or sisters, or father, or mother, or wife, or children, or lands for my name' s sake, shall receive an hundredfold, and shall possess life everlasting.
Luke 14:26
If any man come to me, and hate not his father, and mother, and wife, and children, and brethren, and sisters, yea and his own life also, he cannot be my disciple.*
*Note that we are not allowed to hate even our enemies, but it means that we should be willing to choose God over even the closest of human relationships.