you are out of catchment but your child’s distance to the said school is less than the last child admitted
If there is a defined priority admissions area ('catchment '), then this is sometimes 'within a radius of x miles', but more likely to be an area bounded by certain roads or other geographical features. Is the school set squarely in the middle of its priority area? If not, it is perfectly possible for an IC address to be further from the school than an OOC one.
However, if you have been told officially that the last offer was under Criterion X at distance Y, and you have also been ranked under Criterion X and your official LA distance (not Google Maps or any other DIY tool) is less, than either there has been an error in ranking - or your application was counted as late - ?
we appealed the primary feeder school and where just put on a W/L for 3 yrs despite emotional upset
I assume you mean that your appeal was not upheld, as the outcome of an appeal is either 'upheld' (school directed to admit) or 'not upheld' (school not directed to admit, appellant’s position remains as it was for the duration of that academic year, unless a material change of circumstance means that they can appeal again); the panel cannot enter the decision, 'school must add name to waiting list'. And the appellant pupil being 'emotionally upset' is unlikely to outweigh any but the very weakest of a school case not to exceed its numbers (and absolutely won't be a reason for an independent appeal panel to uphold an appeal against the refusal of a place on the grounds of infant class size rules, if this appeal was in R /yr1 / yr2).
60% of her friends are going to this school so will impact ease of transition and wellbeing if she’s not accepted
Obvious response, What about the other 40%?
If you were an on-time applicant, and you genuinely believe that your DD should have been ranked above the last offered applicant, then you need to pursue this now with your LA, as this should be sorted out before getting to appeal. You can always withdraw your appeal if a place is offered.