Not a solo parent, but I have a husband who can't really be left solo with the kids because his job requires emergency response. I generally have to ask my parents or his parents to come stay with the kids if I go to a conference, whether or not it's over the summer.
They're supportive, but they're also pretty far away, so it's hard to coordinate. I've tried to have the whole family come along with me, and that doesn't tend to work well (but maybe it will now that they're a bit older?). I know some other people who have reliable babysitters that they can pay to stay with the kids for a few days for conferences. Basically, I think you just need to cultivate some sort of tribe - find a colleague in a different department with kids approximately the same age, maybe, and see if you can trade kid-minding duties to allow the other person to go to a conference?