I would have mixed feelings at moving kids of that age, Rudy. I think for your eldest (half way through A levels) it will be difficult, but not necessarily impossible. You will need a school that does Advanced Placement exams, which are acceptable for uni entry in UK, and allegedly equate to A levels (I don't buy this; DD1 is doing at least one AP exam next year, and she's doing the IB as well). S/he will be able to do AP exams in the same subjects as A level, almost certainly, plus a few others as well. I wouldn't think about the IB - it's a two year course - but your younger two could finish GCSEs and then go to a school that does the IB. There are a few schools in the US that follow the British curriculum - the one in Washington DC is supposed to be very good, and there is another in New York, I think.
I have a friend who moved her DD to the US after GCSEs, did IB in the US and loved it, made a great set of friends and has a jet setting career post uni.
Re your Mum, I was overseas when my DDad was having cancer treatment, and it was no fun. At one point I was going back every weekend (a 3 1/2 hour flight, and I had a 5 month old baby at the time).