Enjoy your vacation and don't let anything dampen that. I can't answer as to the insurance questions. It might be a good idea to talk to you broker about this. For vacation time, my contract states that I take a minimum of 3 weeks per year and up to 5 weeks (all unpaid). Most vacations are 2 weeks and under, requiring 4 months notice. For anything over 2 weeks, I give a year. For my 2.5 week I'm leaving for on Wed, I told them last February. I just gave a rough time that I'd be going and firmed up specific dates once the flights became available for booking. Should a trip come up unexpectedly with less than the prescribed notice available, I will ask if everyone's ok with it with the understanding that I might not get to do it. I've not had a problem yet and my clients are always very accommodating. I'm actually amazed that my clients were still ok with me going on this vacation because I just had 2 weeks off before Christmas for a surgery. They were actually very insistent that I go!
They're a pretty awesome crew

I would think that booking time off in April should be just fine. That's lots of notice. Also, which might be helpful for you in the future....when I interview, I make it very clear that I travel at least once every year and like to take advantage of any cool travel opportunities that come my way. They know right from the minute we meet that having solid options for back up care is imperative. I don't take anyone who doesn't have good back up. So far, no complaints. Good luck