Tinyrick very glad to see you have included the children, I think to not do so would be very harmful to their relationship with you and their step father. I am an adult and I would have been hurt if my dm had got married without me there!
Now... "Okay new question...is it okay to just have my kids there and not any parents/pils?"
This is one where I would say if you really do not want them present you do not have to have them. Part of me wants to ask why your wedding has to be so small and private and I kind of see it as a tiny bit worrying that you do see it as something just between yourselves. It is a very alien concept to me as family is so important. And if family is important why would you want to exclude them! I don;t mean distant family, I mean close family.
But assuming you really do want to exclude them, and be clear in your own mind this is what you are doing by not inviting them, then I would see if you can come up with some sort of day which includes a very small private ceremony followed by some sort of party afterwards which family are invited to.
If I were your mum I would be very hurt that you would rather have a total stranger as a witness than me and your father. I would feel it showed you were distancing yourself and your husband from me and your dad. My friend invited only family to her wedding. Her husband-to-be chose to have his best friend as best man. She chose not to invite her best friend.
It took a very long time to heal that rift that that action caused.
Weddings tend to be a occasion for others to celebrate your private love and commitment played out privately in your home and bedroom for thousands of days in your life together, your wedding is one day you share this with your family and friends. I just wonder why you want to not share it with your parents?
Sorry if that sounds hard, I am a mum, a daughter and a sister and I would feel awful to be excluded from any weddings connected to those key features of my relationships to others.