The problem with an operation that you describe is that the ocean does change, and you could have a glassy sea going down, and have to fight 4 foot waves on the way back.

For safety's sake, you will need life preservers for both children. If you have to buy them to get them, then do so.

Make certain that you have plenty of sunscreen and keep it on both of them. I hope that the boat will have a cabin with a head and bunks for them to sleep on. I looks like you will be making a voyage of 60-100 miles. I suggest that you leave the kids at home. I would. If it is too hot, too cold, too rough, or if they get seasick, it will be the longest day you will ever want.

Regards,
Dan

Here's what you have to think about. Say something does go wrong, not likely, but always possible. With the water temps right now, I'd say you have 1/2 hour to survive before hypothermia. Life jackets or not.
By the way - who is the captain of this boat? How is their experience? Do they have a license to operate a boat?

Lots of good advice I see in response to your question. Having raised 3 sons in various adventures, I'd never have taken them boating at that age, even on a lake. That's a long day for children of that age. I can't even imagine anyone holding onto a l yr. old for that amount of time, especially in such tense circumstances. (which the outing could turn out to be) Whether you're speeding or not is not the question -- others are, and if they're water skiing, there's going to be some heavy waves there. Life jackets for a pool is fine; for the ocean, frankly, they are a ludicrous consideration.
You will know the right age as your children grow and mature and are "taught about boating" When you say, "a boat like this" -- that really doesn't describe all the variables.
Your family is too precious to risk an adventure that could too easily turn into a tragedy you'd never get over. As I said, raising children with adventure IS an adventure; one that you want every edge with. I think that being a "newbie" yourself gives rise to your uncertainty and questioning. It is that "inner voice" of wisdom calling you to try and find some sense of safety to your decision to do this. You want to have somebody else say that it is ok, with proper safety etc., etc. But if you really believed this to be a wise decision you'd not be needing the confirmation of anybody else. Listen to that "inner knowing" -- it could save your life someday, perhaps even the lives of your children or some other whose well-being you treasure.