Start with your daughter's contract of employment and any employee handbook/terms and conditions which set out the disciplinary process which should be followed. If the employer appears to have breached their own procedures that is also a ground for appeal she needs to point out - it will be useful if you did end up in an ET.
I would strongly advise that along with criticising the decision as being unduly harsh your daughter makes it clear that she genuinely did not realise there was anything wrong with accepting the invitation to drinks from her line manager and would never knowingly accepted any "stolen" drinks offered to her. She needs to point out her (hopefully) unblemished disciplinary record and examples of hard work/achievements/loyalty etc.
You need to be aware that in considering whether someone has been unfairly dismissed, an ET looks at whether the decision to dismiss falls within what is called the "band of reasonable responses". That can range from a slap on the wrist through to verbal warnings, written warnings, demotion and dismissal. The tribunal will consider all the evidence and decide whether dismissal was a reasonable option in all the circumstances.
For a claim to be successful, a tribunal has to decide that dismissal was a response no reasonable employer would have made - so it is not as straightforward as "fair" or "unfair". If they decide that dismissal was an option, then they cannot overturn the employer's decision.
This explains the point of law quite well:
www.got-the-boot.com/law/law-06.htm
In the circumstances you have outlined, if your daughter has a clear disciplinary record, yes I would say you had a good chance of showing that no reasonable employer would have chosen to dismiss. However, hopefully it won't need to go that far.
Rather than overtly threatening to take the matter forward to an ET, I would advise a strong but subtle approach in your letter of appeal. You will have more chance of success if you allow the employer the chance to review their decision to dismiss without it being a complete and embarrassing climbdown.
You will find the ACAS site a mine of useful information to help you with the appeal and your rights:
www.acas.org.uk/index.aspx?articleid=1390
If you do end up having to make a claim to an ET, do read up on it first:
www.direct.gov.uk/en/Employment/ResolvingWorkplaceDisputes/Employmenttribunals/DG_10028122
Good luck!