the local schools in sta eularia are fine as far as i know.
the background you've got will help you skip a few stages of the process in terms of everything. however, you will still need to, or it is advised to, get an NIE for your kids, then get them empadronado, this things will count as points to your application.
6 and 3 is fine, they'll get given additional, free, after-school support with catalan and/or any areas they are struggling.
the process is that you need to apply in person at your first choice school around april/may. but it's advisable to go to the education office on via punica in ibiza town and they can give you an idea about availability of places in schools. as there are a few in sta eularia, it should be fine. if you were aiming for a village school (like sant josep for example), then it's much harder to find a spot.
when you apply, you put 2nd and 3rd choices in. the truth is that you're likely to be towards the bottom of the list (siblings, low income families, etc get higher points) but there will be a space for them. defo worth going to the education office as they can tell you which school has places for the 6 year old and you can aim for that one.
in case you didn't know. kids start school here in the year they are 3 (kind of like nursery equivalent in UK) and there is 3 years of this. then in the september of the year they are 6, the formal Year 1 begins. so your 6 year old is quite likely to have a head start academically, which should mean they can concentrate on the language.
also, the year you go in depends on the calendar year, not academic. in other words, the oldest kids in each year are born at start of Jan and not start of Sep. not sure what difference this makes to your kids.
about morna, it's really not right for young english speaking kids to go there. as most of the younger kids there now are spanish, so much time is spent on language basics, that english native speakers won't get anywhere near the standard they would in a state school.
in other words, the school my kids are in, when they started they were the only ones who couldn't speak spanish and catalan. so they had no choice but to catch up and achieve the standard level of the class. at morna, as so many have the language barrier, it's slightly different.
at the state schools they teach in catalan. my kids have been in school 2 years and are now both fluent in spanish and catalan. homework can be a bit of a challenge sometimes (for me i mean!) but it's really no different than if it were in spanish. i think it's great they are getting to learn catalan fluently and it's really no extra burden for them. when they come to it, learning french will be a doddle.
good luck with everything.