Dating someone with kids?

So this one is more specifically for girls because I want to know their opinion on this. So I have a two year old and I have one on the way, and these are both from the same girl who is my recent ex. We broke up after a 5 year relationship that was bad for about 4 years of it. I am not looking for anything now but I know I will have to deal with it later on.

Is being a single dad (we are splitting custody of kids so about 50-50 time) a deal breaker for most girls? I know I'm not the most attractive person, but I am a very mature nice person, however I'm afraid it will be a turn off to most woman especially because I will put my children first ALWAYS.

What are some of your thoughts about this?
Dating someone with kids?
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