I don’t think it’s proper that the cousin be inserting herself into his life day n night. That is extreme. She should not be constantly interrupting family time. God first, then spouse, and children, then others. I realize she may be lonely. She still needs to have respectful boundaries, and develop other friendships.
I would have an honest discussion with my husband about why the cousnin is so “in to him?” Some guys don’t always see it when women are flirting with them. Does the cousin meet an emotional desire in him to feel needed? Does he or the cousin feel an attraction, even if it’s just an emotional closeness? Point out your observation that you feel this cousin is taking #1 place in getting his attention day n night, while you only have a few hours of opportunity. Maybe only 30 minutes over dinner, before each goes & relaxes doing what they prefer.
I would encourage my husband to text, “Spending time with my wife, and family, Good night” and then put the phone down each evening. He needs help setting healthy boundaries. It is one of the ways you protect your marriage by putting it first!
I like the idea that you may become her friend too! Women have a lot more in common! A friend who is willing to take the time to stay in touch is nice.