Do you feel able to post all the words of the admissions criteria + any notes associated? (I don't think it will identify the school as many RC schools used similar criteria)
I think you might be right that if it says "baptised catholic children or those enrolled in catechumenate" it is (not very clearly) saying it means the child not the parent who needs to be enrolled - but you are right that children under 7 can't do it anyway, so it makes no sense.
The crux of the argument is all around if you and DD could both be considered "catholic" at the time the decision was taken, which is why the exact wording of the criteria is key.
The key points in your favour are the advice from the priest that this is what you had to do for you & DD to be considered catholic & the head saying you would be in cat 2.
I would see if your priest could draft a letter supporting your appeal, explaining what you have done & that you & DD are now fully fledged catholics in his opinion (stressing the weekly mass attendance for good measure )
The head probably won't be able to "support" your appeal (this is usually school policy) but often they won't put up much of a fight (IYKWIM ) if they agree the appeal should succeed, so I would have a chat with the head too.
As you have completed RCIA you are now a fully fledged catholic & (if I understand the "conversion" system correctly) DD is being raised catholic & is now considered catholic too (as she is a baptised christian, below the age of reasoning & you can't baptise again as RC) so also ensure that the school have you on the waiting list at cat 2 now, just in case any places come up ahead of any appeal.
There are never any guarantees at an appeal, but I think you do have a chance. Is it an infant class size appeal? (30, 60, etc in a class) these are always harder to will, if it's not ICS, I think you have a very good chance of success.