PIP appeal

Hi. Six years ago, largely thanks to the information on this wonderful site, my daughter, who has a diagnosis of paranoid schizophrenia, was awarded the lower rate of daily living and, after an appeal to a tribunal, the higher rate for mobility she had initially been awarded nothing for mobility by the DWP). Almost three weeks ago, she received the decision on her renewal. This time she was awarded the higher rate for daily living (which I agree with though some of scores seem anomalous) but only the lower rate for mobility. We had assumed she would continue to receive the higher award as she goes to medical appointments regularly (she has to attend a clinic once a month and also has occasional doctor’s appointments). She always needs to be taken to these and have a family member with her during the appointment because of her unremitting anxiety at being with other people. She also does sometimes go out with family, though this is rare and inconsistent, and she will only ever go when pressed to do so by her husband or me and is always escorted. At the time of her first award she was attempting to go out a bit more but she was attending far fewer medical appointments so we considered overall her practical ability to go out was little changed. But the moderator said the descriptor 1e (unable to undertake any journey because of overwhelming psychological distress). I thought this only applied if someone never left the house at all.
The moderator actually phoned her husband (who has become her appointee) on another issue (she is owed some PIP money and he needed to check details) and said she would be getting the lower amount as the law had changed since her first award. I know of the changes that took place as a result of the Upper Tribunal decision (CPIP/1347/2015) with the government changing the mobility descriptors for psychological distress in response to the Tribunal’s decision and then having to backtrack in January 2018. I know of no other changes that would effect a change in my daughter’s eligibility for the higher award. It is as if the moderator did not count journeys to medical appointments or very occasional outings,
If we are to appeal, we have to do so by 7th September. On the basis of the information here, is there a reasonable hope of an appeal being successful? And if so, can we include further information on her occasional outings to clarify what was written in the original application.
Thank you in advance for any advice or clarification on the law that you can give. We are extremely grateful for all the help you give.

Thank you both for your replies. I should have made clear we were considering whether or not to ask for a Mandatory Reconsideration. We actually did go ahead with the MR and have just received a letter awarding her the higher mobility rate. I think this is probably for three reasons:
1. We stressed the tribunal decision 6 years ago and the fact that her inability to go out unless accompanied is unchanged.
2. The regularity and frequency of her medical appointments.
3. For some reason, we had omitted to mention in the original application that, because of her social phobia, she cannot stay in her house when the cleaner is there. The cleaner is paid for by by us, her parents and comes once a week, so every week we (her parents) collect her and bring her to our house, which is only a short walk away. We were not sure they would take this regular journey into account as it was not in the original application, but I think they probably did. A lesson in ensuring we include every relevant detail.
I must, once again, thank the Benefits and Work website for the fantastic, clear guides and advice, without which we would not have been able to really get to grips with the whole process, first or second time around.