I got married twice, it was a second wedding for us both. I was told I couldn't wear white, couldn't have a big wedding, couldn't have showers, it was tacky to register, etc. Don't listen! This is a new marriage and new beginning for you both. Celebrate it the way you want!
I would have bought a white dress if I hadn't fallen in love with a pink one. Pink is my favorite color, so the sparkly pale pink dress was perfect!
I did not have any showers and I wish I would have. Regardless of the gifts, showers to me are just time to spend with close friends and family to celebrate before your big day. I would have LOVED to have a shower for that reason, forget the gifts!
I didn't have a bachelorette party because I had been married before, I regret that. It would have been nice to have a spa day with friends (no going out necessary!)
We did register, and that was wonderful. It helps people to know what to buy.
I don't think a second wedding need be small or inexpensive if you don't want it to be. It shouldn't be "embarrassing" to be married a second time! You're paying for it, it should be the party you want! My mother spent a lot of time making me feel like I had to be low-key because I already "got a wedding." I threw those pictures away. This is what I have pictures of now, this is what I'll be showing my kids and grandkids. Luckily it turned out to be exactly the wedding we wanted (I didn't listen to my mom on everything!) and I have wonderful memories!
As for the cousins of your ex--why not invite them? If they feel uncomfortable they'll make their excuses. You could even hand-deliver their invites and say "I would like to share my special day with you, but if you feel uncomfortable, I totally understand."
Congrats!