This is going be pretty daunting, but here is a "starter for ten". Looking specifically at your son and the grammar option first, then the other options, this is what happens:The grammar option
:: He has to be given the right to take the 13+, based on academic evidence submitted by his current school. From what you say I am guessing that you have already applied for that? If he is refused the right to take the test (which seems unlikely) you can appeal against that decision.
:: He then has to take the test and qualify.
:: If he doesn't qualify you can appeal against non-qualification. The Appeals Q&A Section B describes this process. http://www.elevenplusexams.co.uk/appeal ... lification
:: If he qualifies he will be offered a place at the nearest grammar school that has an immediate vacancy. Hopefully that might be Sir Henry Floyd, and AGS might just turn up with something, but it could be another Bucks GS - even Burnham! Places in Year 8 are not that common, so it will be touch and go. I suggest that you call the schools, ask to speak to the Admissions Secretary and establish the current position to give you an idea of what might happen if he qualifies.
:: If there is no immediate vacancy you can ask for his name to be placed on the waiting list for your preferred schools in the hope that a place may turn up during the summer term.
:: You can also appeal for a place at AGS and SHF (two separate appeals) - an over-subscription or "transfer" appeal. Appeals Q&A Section C: http://www.elevenplusexams.co.uk/appeal ... bed-school
:: Even if neither appeal is successful his name can remain on the waiting list for both schools.
:: Now to the biggest problem. If a GS place does not turn up by the end of the summer term, he will lose his priority as an in-year admission and be joined by all the children who have qualified in the main round of 13+ testing this year. (The test is taking place next weekend.) As you live 8 miles from Aylesbury, there are likely to be a lot of children who live closer to SHF and AGS, and he may drop quite a long way down the waiting list.
:: As a last warning, a 13+ qualification is valid until the end of Key Stage 3. In some schools that is the end of Year 9, but there are schools where KS4 starts in the summer term of Year 9. However that is more than a year away, so let's put it to one side at the moment! The upper school/comprehensive option
:: If he qualifies in the 13+ but there is no GS place available, Bucks CC will automatically allocate him a place at the nearest available Upper School. That might be The Cottesloe, but it might be a less appetising option.
:: You can appeal for a place at a different Bucks Upper School (or schools) if you wish, and you can also add his name to the waiting list for any Upper Schools that you prefer to the allocated school.
However at this stage, the Herts schools become relevant. People are suggesting Tring for a good reason. It is a sought-after comprehensive school and probably better than any of the Upper Schools in the Aylesbury area. So:
:: You should call Herts CC and apply for a place through them, with Tring as your first choice. The school is likely to be full, so once again the next steps would be an appeal & the waiting list. As you are very close to the edge of the catchment area you will probably find that he would be pretty high on the waiting list.
:: I am not sure which school would be the alternative one allocated in Herts, but it is worth asking Herts which the nearest school to you with vacancies is.
Lastly, for now at least, everything above applies to your daughter as well, but AGS becomes AHS.
If she did take the 13+, would she get any extra time or anything with her dyslexia? We do have a psych Ed report fr her, though it could do with updating as its about 3 years old now.
You can apply for extra time, but the EP report would need to be renewed before you did so. Extra time is not given readily, so don't pin your hopes on it.
I would ask around/call the schools and talk to the SENCOs to establish which ones have the best resources for dyslexic children before making a shortlist of where to apply. I believe that Tring might be top of the list on that front.