I used to cope with visiting mum by stapling a "mask" onto my face and going in with a bright and breezy "isnt-this-all-very-nice" attitude. I found that mums mood would mirror mine, so if she realised that I was upset, she became upset too.
It became a sort of Fake It Till You Make It exercise and I did find that it became easier with time and as she settled. Im guessing that your mum hasnt had long in her care home and probably isnt yet settled. I found mums care home quite alarming to start with and didnt know what to expect, but the mask stayed on and after a while I got to know the carers and the other residents and their families and it all became easier. I started to relax and chatted to everyone else around as well as mum and they became more like an extended family. I found a sense of humour helped too.
Mum thrived in her care home and became content there. She made friends too, so it definitely became easier. She had 2 good years there and I was able to take her out for a few hours (got less as the dementia progressed) to a local garden centre, a cafe or I would push her wheelchair along the sea front.
Try to hold the tears back until after you have seen her, have a good cry in the car park where she wont see you and then go and do something nice for yourself - even if its only a coffee and cake at a cafe. It will get better, I promise. ((((hugs))))