I had a situation like this with my first dck who started with me at 15 months. I just had her and my two kids, but for the first two months she cried and screamed a lot and would push my daughter away or try to kick her and wanted me to hold her all the time. She started part-time and it improved a bit once she became full-time as things got into more of a routine. I started ignoring the crying and refusing to pick her up much of the time and eventually she stopped and adjusted. I was very firm about her not pushing or hitting the other kids, which was I think, out of jealousy and insecurity. Once she understood that her behaviour wasn't getting her anywhere and also once she adjusted and started napping well etc, things improved a lot. In fact, 5 months later I am happy to say that she is now one of my best behaved kids I think part-timers take longer to adjust and can act out because of insecurity in their new environment and jealousy of the other kids.