Where you decide to move to does not affect your children's school places if they stay in the school. If you have a younger sibling not is school at present then this may cause issues when you apply depending on the admission criteria of the school.
However if you are expecting to move schools when you move house then you have to accept that many of the schools will be full or only able to offer a place to one of your children. Your younger child in year 1 will also potentially have the issue of any appeal being an in-year infant class size case which will be incredibly difficult to win. So I think you need to accept that any house move may well end up with you not having a great choice of schools for your children and that appeals for both children will be difficult to win. Your actual address does not stop you applying for a place at schools in any LA and a place will be offered if there are places available. When you can apply for a place will depend on the arrangements in place for in-year applications. Some LAs say you can only apply when you have actually moved, some are more flexible.
You do not have and will not get information on in-year admissions for schools but you can ask individual schools and the LA involved whether there places available, at which point many will say they are full. By the same token you will not be given any information on the number of appeals which are upheld or rejected that are "in-year" appeals