How to date responsibly?

So I'm sort of seeing this guy... he has two daughters ages 2 & 4. My son is newly 2. We both have 100% custody of our respective children. However, we are not exclusive and I have been asked out by other men, some of whom I've accepted. I don't really like how quickly things have escalated with this guy... we'll call him Phil. If I ever sleep over I feel so guilty about how confusing it must be for all three kiddos. Whenever I'm there we have a sort of "family dynamic" that makes me uncomfortable. I do like how easily our lifestyles seem to mesh, but we've only been seeing each other for a month. It's especially disturbing when the girls call me "Mommy" or Alex calls him "Daddy" and it's more because I refer to him as Daddy to the girls and vice versa for him with Alex. Their mom is not really involved and so I know they are looking for something to fill that void, and I love all the bonding, but I'm just worried about the consequences if we were to not work out, especially since we are nowhere near a committed relationship... or really any relationship.
Originally I had planned to not introduce Alex to a barrage of strange men, but that seems to be exactly what I am headed for. Yet, I feel that if I were to keep Alex away from my love life, it leaves little time for him and I feel like I'm neglecting him, especially since it's been just us for almost two years now.
How should I approach this and what should I change when dating other people? I'm trying to mix what's best for Alex and what's best for me, but more and more I find myself looking at a black and white... is there a way to find a happy medium?

You wouldnt be neglecting him if you werent include him in your love life. I have made that mistake with my son by getting him involved with my love life and I realized that it was a mistake. I would feel really iffy if his kids were calling me mom.

You need to think what is right for your son. I wouldnt introduce him to every guy that you are thinking about being with.

Quoting Yurvette [♥]:" You wouldnt be neglecting him if you werent include him in your love life. I have made that mistake with ... [snip!] ... You need to think what is right for your son. I wouldnt introduce him to every guy that you are thinking about being with. "

It's just so difficult because I don't always have someone to watch him, so when I find a guy I want to spend time with, I either don't and give him the impression I don't like him or I do and involve him in Alex's life. Argh... I hate catch 22s...

Quoting Megarielle:" It's just so difficult because I don't always have someone to watch him, so when I find a guy I want ... [snip!] ... I either don't and give him the impression I don't like him or I do and involve him in Alex's life. Argh... I hate catch 22s..."

Or you can wait until he goes to bed. That is what I do when I have started meeting someone. Had them come over after my son goes to bed. I know how it feels like.

Quoting Yurvette [♥]:" Or you can wait until he goes to bed. That is what I do when I have started meeting someone. Had them come over after my son goes to bed. I know how it feels like. "

This. I'd wait until the kiddo goes to bed and have a movie night. If things keep progressing and he is patient and understanding, then things can progress further.