kids and dating

how long would you wait before bringing another partner around your kids. my SO has a child with his ex and she has a child with her ex husband. while she was married she had 2 affairs that we know of and was taking both kids around these men. the last guy she had an affair with she stayed with him and ended her marriage to ex husband. seeing as how she jumps from guy to guy so fast he isn't comfortable with her taking his child nor my step daughter around these men she hardly knows. And before any one gets on this ex husband still takes care of my SD he has her and his child most of the time when it's mom's time with her kids. he has told her his child isn't to be around these men until she has been with them for a good amount of time. my SO agrees with that as well. but she has told the both kids not to say anything or she will introduce them as her friend. my SD is very loyal to her mom so she won't say anything but slips up sometimes and her sibling tells ex husband everything. just to give a description affair # 2 only lasted about a year engaged at 6 months but broke up because she was cheating on him. She is now with another guy and the kids have already met him found out because steo daughter slipped up and then EX husband confirmed that his child has said something as well about a "new friend" that mommy kisses. my SO and ex husband didn't ever meet affair #2 guy and have not met this guy either. both want to put a stop to her just bringing men in and out of the kids lives but don't know how to go about it. with her history they both think it's fair to say that she should be with a guy at minimum a year but will settle for 6 months at least and both want to meet the guy before the children do. is that too much to ask for?