I have cms vCita which I use for all other scheduling and payments.

They have facility for me to shae documents, but I do not want to share word documents. Can I upload JotForms into my document account in there and have clients be able to fill them out and submit them back into vCita? I would also like to be able to print my forms if required in person.

Though we do not have an integration for vCita, there is a third part integration through Zapier that will allow for creating new clients in vCita from JotForm form data.  Here is that integration:

https://zapier.com/zapbook/jotform/vcita/

I am not sure the extent of the integration so you may want to contact Zapier if this is something that interests you.