Parsing HTML Tables that requires login

Does anyone know how to Parse HTML Tables that requires login. I would imagine that if you want to automate this process I would need to run two programs. One to login into my site and the other to scrape the data.

I think I would then need to run another program to collect the useful data and insert it in my SQL.
What I want to do with this is to start using Square Cash for payments and have the payment info posted in my square cash dashboard dropped into my WP Appointments SQL and turn the confirmed status to paid with the amount and payer info.

Does anyone think this could be done? I probably need to hire a programer, but is this worth pursuing? Square Cash does not have an API.