Has she got a boss or is she the owner?
Firstly, the probation period is a red herring; now you have to be there two years before you can take anyone to a tribunal for unfair dismissal so forget about keeping your head down and then letting rip.
So; lets tackle the issues separately.
Saying one thing and then saying that she didn't say that she said this...
Note down in your notebook word for word what she asked you to do. then send her a follow up email saying 'Hi boss, just confirming that you asked me to do this by that date in this fashion'. Once it is completed, make sure that you email her with the original email at the bottom saying "Hi boss, just to let you know that X is done now'.
Record in writing each and every request and read it back to her as you have written it. Then do the email thing. If it comes to it then you can say 'I emailed you on x date to confirm your instructions and I didn't get a response, if I had understood them wrong that was the time to say so. I wrote down word for word what you said and also read it back to you'.
With regards the phone thing: if you don't work on Wednesdays email/say to her on Tuesday lunchtimes 'Is there anything pressing you need me to do before Thursday so that my work is covered on my day off as I can't take work calls on my day off, if so can you let me know by 2pm so that I can ensure it is covered'.
If she does call, and you do answer the phone, say 'I can't do any of that today as it's my day off. I'll have to deal with it when I am back at work'.
If she says 'It's urgent and you need to do it' you need to say 'Well, if you need me to be on call Wednesdays then we need to discuss an on-call arrangement and a work mobile phone as I will have to pay for childcare as Wednesdays is my day off and I am usually with my child on my day off'.
You have to cover your back and set those boundaries now without pissing her off. Once she knows you note down everything word for word, and email her your instructions she might well stop leading you up the garden path.
And if she doesn't - you might just have to find another job.