Bad experiences but want to continue as a career

Hey, this is my second year of working in the industry and I love planning activities for and with the children and also helping them grow. The first company I worked for i resigned because staff were to bitchy and practises were poor. I have started at a new centre where u can see that the educators are there for the children and generally love there job. Also a tight knit team. Last week i was accused of lying by the manager to Which I did not. ( I didn't know i started early one day as my roster changed and I wasn't told this shift was now an early, and i said this but she is convinced i did know and just forgot but won't admit that) then last week i was accused of lying to a parent (I said I don't know and will check that information for you as I was on lunch. Turns out I wasn't on lunch but I didn't lye I I though I was on lunch .) Now i cannot talk to parents until I gain the educators trust back. She even brought up how we have to be honest, build realtionships and trust. I thought i was building relationships with educators and I ask for help and follow the routines, use initiative and step in where I can , I don't know where I screwed up. I honestly want to gain their trust back and do the right thing ( but will not admit i lied as i do not believe I lied in these circumstances) I have apologised and said that I will try but how do I do this how do I gain their trust back ?