If the issue is that the bank won’t let you manage the account, rather than the private pension not agreeing to make payments ..
Do your parents have a joint account? If so, your mam can complete the paperwork making you a “third party” to the account, this wouId allow you to manage both their finances (with her consent).
The private pension only need an account to make payments to, so long as the person who should be receiving the payment is on the account, they should make payment. They should be able to make payments into a joint account held by your parents.
If you then want to separate the monies to make it clear for social services etc, but are unable to open an account for your mam elsewhere, due to lack of ID, will her present bank not open one for her? Or does she not hold any accounts?