Do you have the text of exactly what you submitted as your appeal?
The issue here is that ParkMaven have issued 2 separate charges, one for each day - the signage probably outlines that they can do this (but worth checking if possible). As they are two separate charges, ParkMaven will say that they need appealing separately.
Do I contact the debt collectors? I really don't trust them to even care.
Indeed they won't. Debt collectors don't care about anything other than collecting payment. Ignore them.
Do I just make a firm stance with ParkMaven and tell them their system is the issue as i notified them of original payment for both of the days.
It seems like the issue might have been with a mistake being made when the driver inputted their reg, rather than ParkMaven's system? But you could take a firm stance with them that this is a minor keying error and that per the BPA code of practice they should cancel the charge. If you are planning to fight it, you may need to be prepared to go to court (a typical loss in court is around £220 for a single charge).
Is it worth me contacting a solicitor?
You're unlikely to find one who costs less than the value of the parking charge.