I can understand your reluctance to embark on extra administration, but without it you have no legal authority to manage your mum's affairs. Your access to her bank account is based on permission from the account holder, which is only effective while she has capacity. The Court takes a dim view of anyone informally operating the bank account of someone who has lost capacity, and it is probably against the rules of the bank also.
If the application has been refused by OPG then they will be aware that your mum has lost (or may soon lose) mental capacity. I would have thought that without a valid LPA then OPG would recommend to the Court of Protection (COP) that a deputyship is required? Once the COP has been made aware that someone has lost capacity and has no-one authorised to manage their affairs, then the Court has a statutory responsibility to put delegated legal authority in place. Check with your solicitor of course, but I don't think an informal arrangement is an option any more.
I hope your solicitor can explain why the OPG has rejected the POA application. It may be because it has conditional arrangements in it, e.g. decisions about expenditure over £5K. They don't like these, and sometimes such provisions are struck out. If too much of it has to be deleted then it may make the whole POA document invalid.
Alternatively, it could be that you sent in a LPA in the old format, which had to be completed and signed before 1st Jan 2016 in order to be valid for registration. If this is the case and your mum can be deemed to have capacity in the moment, as others have said it would be much easier for you to get a new and simple LPA form signed and sent off for registration.
Being assessed as not having mental capacity can mean many things. In terms of her welfare and living arrangements this may have been the conclusion of best interests meetings, supported by reports from various professionals. However, a solicitor may decide that she does have capacity to give instructions for a POA because in the moment she is clear and consistent about her wishes. My mum's solicitor took this view because when she visited my mum in hospital on two occasions the instructions were consistent and clearly expressed. My mum was quite frankly away with the fairies at that time but she was very clear about who she wanted to be her attorneys, and who she did not (me! and that's another story). Talk to your solicitor.
It may not be too late for POA.