How old are the kids then?

Their free pass is obviously linked to yours-so not available to others. Some railways have special deals for adult+kid-other/most simply then want the kids to have kid-tickets. Also-again depending on age of them-several railways will not want all their precious seats to have people sitting on them without even minor payment-so they refuse to do that-take them on your lap is the message.

Hello thank you for your reply…

I was planning this:

1. Get two EUrail passes for me and two free for  kids
2. Purchase and reserve 4 seats for each trip we do
3. my cousin are traveling without a pass but they would take the kids
4. I would reserve and purchase seat for my kids, but I do not know if they can travel without us

As the kids' passes will be linked to your passes the kids can't travel with only seat reservations without you. 

When the kids travel with only your cousin they will need to have the appropriate children's ticket for the country they travel in. Which countries will that be?

ok, so I will have to buy them a regular ticket, right?

Paris london

Here you can read about children’s fare on the Eurostar.

https://www.eurostar.com/uk-en/travel-info/your-trip/travel-with-children