While I'm in a similar situation to kml (my children are adults), I disagree with her. My kids are out doing their own thing, but I still put on my profile that I have kids (no pictures, just a mention) and even grandkids (again, no pictures, just a mention). I think if your kids are adults, it is fine to leave them off, like kml said, but if they are under 18, it seems a little dishonest to me to not at least mention them because odds are that they are staying with you at least part of the time so that is a very real part of what your time is dedicated to.
I think the small place you live might be a bigger factor than you think. I had that same issue as well initially. I live in a very small town and originally, I had the location set to a very small surrounding area and I was getting NO hits. Once I expanded my area a bit to include some larger cities nearby me, I got more "traffic" so to speak.
If you think it is about the kids, then you have to do what you think is right and I am only speaking for myself here, but because I'm a mom, I didn't mind coming across men with kids. I actually preferred it, in fact. And, honestly, if I liked a guy initially from his profile but I didn't find out until later that he had kids, that might give me a little pause, wondering why he hid that, even if he wasn't necessarily trying to be deceptive. I'm sure that makes no sense and I sound crazy now, but hopefully you get my point.
Me 52, H53 Bomb drop 9/29/2014 Divorce from XH final 12/17/2014 Marriage #2 12/31/2019 5 adult (step)daughters (3 from XH's first marriage, 2 from current H's previous relationships) 6 grandkids