A very positive 'yes you must go' from me. It is hard but your well being is important not just for you but for your Mother too. You need to avoid a break down which is very likely if you do not have a break.
Try to get someone else to actually transport your Mother to the place of respite, a friend or taxi. It is less likely she will make a fuss in front of them, and even if she does you will have someone else there to understand. I suggest you do not tell her until the last minute, even discreetly packing up her clothes etc.
My SW was not the sort but some will actually take this on and take the sufferer into care on your behalf, even on pretence of going to a hotel for lunch, the day, or whatever white lie suits.
So please do not back out and let us know how it goes.