My mum can be very manipulative

Me and my mum argue sometimes like all people do with their parents or kids, however over the last year or so when we have argued they seem to be worse than any arguments I remember from being a kid. To the point where I realise I am not wasting my time or energy arguing so I just end the conversation etc and won't speak to her or if I do I will only give her short answers.
The issue I have is when we haven't had an argument we can go days or nearly a week without talking which I have no issue with but when we have had an argument my mum will constantly ring me to the point where I am starting to feel like she is manipulating me or gaslighting me. For example, I have never once asked her if I can use her tumble dryer for my washing and she has never offered, but she offers it to my sisters all the time, but now that we had an argument a few days ago she is constantly ringing asking me to take my washing to hers and quite frankly I have no desire to talk to her at the moment so just said thanks but no thanks.
But when I do stuff like that she then acts very upset and sort of gives the impression I should be apologising to her even though she was the one who upset me first and never says sorry. If she said sorry it would make things a lot better and a lot easier but I just can't be doing with her being overly nice with me.
Should I approach this subject with her or just leave it?