Would she expect a doctor to be communicating with other patients while trying to do a medical appointment with another patient?
Would she expect a police officer to answer phone calls while out investigating in the field?
What about a therapist taking client calls while working with other clients?
Does she even understand what you do, how you work (that she's not a fellow employee, you're a supplier to her company as a freelance)?
Not rhetorical questions, she may need it to be spilled out what the normal way of working is.
What you have described would be untenable for most freelancers - if you're saying they're 30% of your client base, she's acting like she has 100% of your work hours on call.
You need to politely and bluntly set her straight. Coupled with rigorous and unrelenting boundary setting i.e. do not answer her calls outside agreed next catch up times, and ignore voicemails between catch ups. Call her out on it if left "no I haven't listened to your voicemail, we agreed to catch up now at 4. So shall we crack on or was your message more important?"
If that doesn't work, you need a "rules of engagement" session with her and the invoice payer. And you need to decide whether to charge them as if you're on an on call rate, or fire the client.
Why are you giving her 100% availablity when they're paying for 30% of your time? You need to put your business head on because this is nuts even if you were an extrovert who likes chatting.
Ignore an poster suggesting you drop hints or make a joke - it's unprofessional, just deal with it as a business problem, she's not a mate, you are a supplier.