Any monitoring app kind of fights against the privacy and security controls that any modern phone has in place, so that is a bit tricky.
I would probably make different recommendations depending on age. How old is your son?
Have you contacted Bark’s support about the problems you’re having? That would be a good starting point if you haven’t already.
Are you familiar with the parental controls built into iOS? You might want to take a look and see if some of that accomplishes what you need without other apps. https://support.apple.com/en-us/HT201304