Well... that will be a lot of advice! I willt ake a stab at it.
We did not tether our babies. We just kept an eye on them. Boats, in my humble opinion, come out of the box fairly baby proof. Areas to watch out for are the panel and them being able to get up the companionway stairs. If it has an electric head and the kiddo has matchbox cars... well, that did not turn out so well for us either!!
You will find that keeping the kids cool will be the biggest difficulty. Lots of water is great. Keep them wet and hydrated and cool.
We used a car seat typically in the cockpit for when we needed them in a controlled environment. We are big fans of Mustang life jackets if you can get one that size. That was what we used for our kids. You need a jacket that will float them face up, has a crotch strap, and a grab handle should they fall in. Most traditional jackets have none of these qualities.
If there is a suitable V-berth, see if you can get a board to go across the berth. We used one with Chase. In the picture below, you will see my mom (taken about 8 years ago) holding Chase.
Over her shoulder you will see what looks like a crib side that actually was a simple board we made to go across the berth (like a crib) so that he could play in there safely while we were under way. However, for sailing or when sailing, the boat will get hot and unless you have a generator and a/c, you will not have them down there much. Plus, you might be dealing with sea sickness if you keep them (or yourself) down there in any type of sea. SO I suggest your car seat or something similar which can set in the cockpit under your supervision and some toys for your child to play with. You can also hold your child (something we did a lot). In fact, that is why I am such a huge proponent of a husband-wife team both being able to single a boat becuase one person in ineveitably taking care of the child(ren).
As far as sleeping, put the kiddo between you. That was what we did. THe exception would be if you rig up the V berth and put several of the kids in there or if you are ok sleeping in the salon. I personally would not let a toddler sleep in the salon unless under my direct supervision. Our only nightmare was of one of my kids sneaking up the companionway stairs and falling off the boat. Of course, it never happened, I am just saying. I know many parents that have put locks on the inside of the companionway and/or rigged some type of alarm (cans falling off from the top steps, for example) to warn them of their kids going up the steps. We never did, but our kids were basically raised on boats and knew the rules (many times tested) from lifejackets to companionway to going forward without permission.
I think that is most of your questions. Don't make too much of a big deal out of it all. It is easy-cheesy and you will have a blast and remember it always.
All the best,