Relationship in trouble?

my girlfriend and i have been official for about a month and a half now. Im 28 and she's 31. It was going well in the beginning and she was crazy about me. but now its getting more demanding and im not sure i can live up to her expectations. She thinks my parents are to dominating and they can be some times. But i also get along with them and want to continue visit them sometimes. I spend really most of the time at her place and im gonna move in with her next month. She's pushing me really hard to confront my parents about them calling me and texting me a lot while im busy. Im about to finish my that i have left of my degree as well as looking for a job so i`m very busy and i told my parents that. But she's also saying that i have to tell them i need time from them and have to tell them to stop calling me and that i will reach out when i`m ready.I told her that i don't have the energy for that and while i admit i should become more independent i asked her if she can let me do it more gradually. Last weekend Before a dinner with my parents she told me that if i didn't say anything about it that night she would go her own way cause she cant take it anymore. She said it with tears in her eyes. While i did hint at my parents that i will be very busy from now on i didn't have the energy to tell it the way she wanted me to. She told me last night i need to get tougher if not i would loose her.