UK visit visa refusal - need advice before re-applying

My husband and I are both british citizens. I am currently pregnant and due to give birth early September. We applied for my mum to come to visit us on a 6 month standard visitor visa from Pakistan (she would have stayed with us for 2 months only) but the application got refused. She has visited us once before in 2012 for the birth of our first child and everything went well back then. The reasons for refusal were:

To note: My husband and I did attach our joint savings account statements which showed a closing balance in excess of £7000 so they must have overlooked it! We both work full time and have about £1200 left over every month after all our expenses have been paid so funding this visit should not be an issue. *The overlooked statement was returned with the other documents so we know that they did get it.

For the second point- my parents were not aware of this thing called "funds parking" and neither was I. For the new application I thought I would just ask my dad to attach the statement of the account he transferred the money from to the US Dollar account and that would be that but on speaking to him I found out that the money was transferred to his account by my sister who was in the US for 2 years for a Masters scholarship and has returned to Pakistan recently in May. Whilst there she was receiving a stipend of $1500 per month and she managed to save this money and before her return she transferred it to my parents' account. She is completely happy for my mum to use this money for travelling to UK.

For re-applying, my question is:

Should I not mention anything about that account in new application and just attach my father's savings certificates (from which he gets interest every month in cash which he then deposits into his current account) or should I explain the origin of funds in the account i.e. my sister saved this money whilst on scholarship and sent it to my parents and attach a statement from my sister saying she is happy for my mum to use these funds for travelling to UK? I feel like this would make things too complicated but not sure if omitting mention of it completely would work either!

Also, the other savings my parents have were not mentioned in previous application as we didn't think it would be needed as my husband and I are funding the visit - would this be a problem now? Would the fact that the monthly interest my father gets is in cash also impact the application?

Many thanks for your advice and help! I just want my mum here for the birth but don't want to apply again if it will be refused as I don't want her passport to have 2 refusals (one is bad enough!)