My daughter is 6 and first and foremost, i know this sorta thing happens and i should trust my kid but she admitted she lied and the lies she said were obvious lies (will explain later) and im just not sure what to do.

Last night we were in the loungeroom watching a Xmas movie and my husband kept poking her on the shoulder mucking around annoying her.. the kids were all laughing and joining in... anyway, my daughter has a short fuse and went from laughing to annoyed very fast.. understandable though she was probably sick of it lol... anyway, she pouted her lips and went to her room all angry (often has outbursts anyway regardless if there is a trigger or not) and when my husband said he was sorry and to come watch the movie she said no. Fair enough... so like 20 minutes go by then she walks out and says "he touched my private part... just now!" and he had been sitting with me so i know it was a lie and i asked her where she got that idea from. She ran into her room and i followed and asked her "has anyone ever touched your private area?" she said step dad had and i asked her where specifically was it and she said her shoulder and her head. i explained what area the private parts are and she was trying to argue with me that no your privates are your shoulders and head. So anyway, i tried to explain what can happen if you say things like that and its not true or what not and tried explaining where your privates are. She then said her teacher touched her private area (pointed down to vagina) and i asked her if she was serious. She said "no im just angry at my teacher can he get in trouble now?" and i started to get annoyed because i realised she is just saying these things to try and get people in trouble who she may have been upset with for whatever reason. She admitted afterwards that it was all a lie, her teacher didnt touch her and neither did her step dad. She said but step dad touches the babies and im like oh god please explain and she said he changes their diapers and has to wipe poop and wee off their private area... and so now im just like fuck me this kid is not understanding it at all and it concerns me. She ended up apologising to my husband and said she only said it because she was annoyed at him. he said if anyone ever does touch her she is to tell a trusted adult but said by saying these things it can get a lot of people in trouble of ot isnt true. My older daughter informed me that a couple of weeks ago they did the whole "private parts" education lesson at school and i wonder if shes got the idea from this. I know my husband has never touched her, her teacher wouldnt either. She lies a lot about stuff but this is a HUGE LIE. She goes to my ex's this weekend and if she says "step dad touched my privates " he wont even question if it was her head shoulders or whatever he will flip and go to police... which hey its understandable... but im just at a loss now as to what to do about it all

Update... so i contacted my ex and explained it to him and he was ok and said she has a bit of a thing for being a fibber and thanked me for the heads up. He called last night to inform me she told him shes gonna tell me that he touched her too. At this point im ready to have her seen by a psychologist. Her father would never ever touch her and i know my husband didnt and neither did the teacher. She has a huge thing with lies and im gonna seek professional help for her. thanks for all the replies guys. xx