I'm going to try and explain this situation the best that I can...

My SO of 4 years is really close to his nephew (older sister's oldest son), his niece in law (nephew's wife) and their 3 kids (4, 2, and 2 months). The 2 oldest are brats who do not listen (unless threatened to have something taken away) and throw absolute tantrums when they are told no. The 4 year old boy will lie to your face when he knows that you just watched him not do as he was told or do something that he wasn't supposed to. I have tried to explain to him why lying is bad and it doesn't change anything (his parents don't try to correct his behavior). He demands to be played with and when you say "not right now" or something along those lines he will follow you around and hound you until one of his parents gets sick of hearing him whine and tells him to stop. The 2 year old is a tantrum throwing annoyance. I watched in horror the other day as she put something brown and log like (I don't think it was a stick) into her mouth that was sitting in the driveway. I didn't yell (yelling freaks her out) just said it loud enough for her to hear as she was at the end of the driveway and I was far enough that running to her wasn't going to do anything as she already put it in her mouth "sister, don't put that in your mouth that's gross and yucky!" I was the only one outside. She dropped it, started an epic freak out tantrum and ran inside. Her dad came out and asked what happened and I answered "she put something in her mouth, I told her to drop it and no I didn't yell. So, If she's going to freak out like that everytime I stop her from doing gross shit like that please don't ask or expect me to watch her anymore." He seemed to understand and went inside. I heard him telling her not to put stuff that's on the ground in her mouth and to chill out.

How in the hell do I deal with this shit and not intrude on their horrible parenting styles? How do I tell a 4 year old that I'm not going to chase him around the front yard for however long he wants me to? How do I deal with a 2 year old that throws fits for EVERYTHING? How do I deal with the fact that while my SO and I do not ever want kids I can't be around these children as much as he wants me to because of their lack of parenting? My SO is super attached to these kids and I do love them but with all the crying, incessant whining, tantrums, bold faced lying and ridiculous demands I'm starting to dislike them and their parents. I'm afraid to damage my relationship if I bring it up with my SO.

HELP!