This is something that comes up over and over again for those of us with children in poly relationships. What about the children? You can look at things logically and know that there is a positive nurturing environment for the kiddo(s) in question, but when you get the: "Why are you going out with him again? I want you to stay and spend time with ME!" or "Why is Daddy always gone?" or other such blatant over-blown statements about your six girlfriends (? I'm sure I would have noticed that!) it can feel squidgy as a parent. You wonder if your choice of being poly is imposing something damaging on your child. Surely time spent on your weekly date is outweighed by the fact that there is almost no time spent in daycare anymore? Aren't the sibling experiences you're providing going to serve them well in the future? What about the part where they'll likely always feel a little different than their friends?
I've spoken with adults that grew up poly. They're responses to my questions about how they felt about it had a lot more to do with the relationship and personal skills of the parents in question than the specific state of the environment being polyamorous. Just as in any household, it seems that the love, caring, communication and negotiation skills modeled are really the main matters of import in shaping how one feels about the family of origin. I think we're on the right track for most of that.
No matter the relationship style, it is made up of imperfect people. We'll make mistakes. We might even repeat them from time to time. The strength here is that we are all interested in continuing to improve. The focus is on next year being a stronger and healthier experience than the previous year. Not just in our personal relationships, but within the family structure as well. That is something that I can give these children for the time they are with me: the firm desire and resolution to put in continuing effort to improve myself, both as a parent, and as a person.