Hi op you are being very sensible. I've been a single mum for 3 years now. I am not currently active on the dating apps but when I am, I always make it very clear that I have 2 children and I don't want anymore. This means anyone who doesn't want to date a parent, or who wants to have kids of their own, doesn't match with me.
I've only had a few dates and they were all in the last year, I haven't been in any relationships so I haven't got to the stage of introducing kids. However, I would be very careful on who I bring back to my house (even without the kids there), I'd wait a long time before introducing them to my kids, any sniff of a red flag and they'd be gone.
Furthermore, I'd always be very clear that any relationship is for me and for my benefit. My kids don't need a stepdad, I don't want to blend families, I wouldn't move anyone into my home.
I do not put photos of my kids on dating apps, on my WhatsApp profile picture. On Facebook all my photos of the kids are available to friends only. There are no publicly available photos of them.
You don't have to be sceptical of every man you match with. Just be sensible.