You can download a copy of Trafford's admissions booklet for primary schools which contains details of all the admissions policies for the individual schools:
http://www.trafford.gov.uk/cme/live/dyn ... 1CFD06BC51
As Etienne indicated it is very difficult indeed to win an appeal where there are infant class size issues. If you have one or both children in the infant classes (Reception, Year One and Year Two) you could ask the Admissions Department whether there are Infant Class Size issues at the schools which you would like (if the booklet shows an admission number of 30 or a multiple of 30 you can be pretty sure that there will be such issues). Where there are ICS issues if you have one infant age child and one junior age child it would generally be better in terms of chances of winning an appeal to place the infant age child and appeal for the junior age child. Be aware, though, that even for appeals for junior age children the success rate can vary very widely between different schools and authorities.
Have you asked the Admissions Department where the nearest school with places for both chidren is?
Hope you manage to find a viable solution.