I'm not an attorney, but I think you (general) can name anyone you want in your will. But I suppose it's possible that he could contest your will after your gone, if you die first, and vice versa if he does. I don't know if either of you would win in those cases - a lot depends on the laws where you live. But hopefully, you can agree on this and trust each other to honor the decision later on.
Another idea would be for you each to put your assets in trust for your respective children, wherever possible. That way, again depending on the laws, they would probably go straight to your children when you pass (or his when he passes), w/o having to go through probate and so on.
A third possibility is to start giving out some of your assets - you to your 2 kids, he to his - while you're still alive, if possible.
To make this easier, I think it would be best if you and DH kept most of your assets separate. If there's a house you own together or something, that might be more complicated.
Hopefully, posters more knowledgeable about these issues than I will soon be in here...