Booking system on our website

We have a website that is built upon word press. Currently looking for someone who can help us, with regards to a booking system, that our clients and staff can sign into.

We would like a booking system where a client will be able to book childcare, in this case a nanny. We would also like the system to be able to allow the nannies to sign up and select there days that they are available to work and shows there profile to potential clients. This system needs to be able to accept payments and gather sensitive information from the client while keeping it safe.

We would like the booking system to be able to compatible for app usage also. The app will need to be built from scratch also.

I don't know whether this is possible or if the technology exists