Ugh, it's so hard, isn't it? I was one of those moms who could never stand to hear my children cry like that, so I took them EVERYWHERE with me. But I was willing and able to do that - many moms aren't.
I have been a childcare provider for many years, and I can tell you that 1) it's the normal age for separation anxiety; 2) she most likely is fine a few minutes after you're gone (if the workers there are any good at their job!).
If you can handle the separation and don't feel guilty about her crying, then you should first ask your son why he thinks she is crying. "You always have fun there. I wonder why sister doesn't like it and cries so much?" He may tell you that she doesn't cry the whole time, or he may say another child is bothering her, or one of the workers isn't nice, or he may just say he doesn't know. : )
Then, if everything seems fine with his answers, tell her that mama is going to exercise and will be back soon. Give her a kiss, and walk away. Trust that the childcare staff will handle it. It may take a while, but this phase will pass.
What I have recommended to some of my parents who have to use childcare but just CAN'T bear to leave their child crying like that, is that they put time and effort into the adjustment phase. Start out by going in with her for 10 - 15 minutes and playing, then tell her it's time to go home, and both of you leave. Next time, take her in, play for 5 minutes, then say you have to use the restroom, and will be right back. Leave her for 5 minutes, then come back, like you said you would. When you return, whether she was crying or not, play another 5, then tell her it's time to go. You don't want to come back and take her out right away, as that will reinforce the crying behavior.
Each time, extend the time you are gone, and keep your time playing with her at 5 minutes or less. She will learn that M. always comes back. I know this method takes a couple weeks, but it does work. At least, it always has for me and the children I watch.
Best of luck to you!