Hi Daisy. Some thoughts.
Your POA must be the older type called Enduring Power of Attorney. For this, you the Attorney are required to formally register your POA once the donor (your mum) has, or is beginning to, lose mental capacity. See this link:
https://www.gov.uk/enduring-power-attorney-duties/register-an-enduring-power-of-attorney
However, potentially you and your sister want to have joint and several POA, which would mean your mum would have to grant a new Lasting Power of Attorney (these have to be registered from the start)
https://www.gov.uk/lasting-power-attorney-duties.
She could still grant POA provided that she understands in the moment what she is doing.
Do you think she would want your sister to be her Attorney? Perhaps you should be talking to her about it? She is the one who must agree to that change, if she has capacity to do so.
I can also foresee there being a possible delay between one and the other, but you'd have to check with the Office of the Public Guardian about those sorts of transitions from EPA to LPA; it might be more straightforward than I think.
Has the solicitor explained why s/he won't release the original? If you choose to register your existing EPA you can enclose a certified copy but in our experience they will only accept this if the original is lost. We had to get the original EPA document from MIL's solicitor; OPG refused to register the POA without the original.
Do you think the solicitor has lost the original? Perhaps if they have no good excuse you could start by getting advice from OPG and take it from there? Knowing that you mean business might be enough to get the solicitor to be more helpful to your mum who is, after all, the solicitor's client.