Effect on citizenship and at POE with arrest/criminal record

[mahi79]

Me and my family had plans of relocating to India in 2010, in the meantime I got arrested on shoplifting case under class C misdemeanor. We had consulted lawyer and had to postpone the travel for 2 months ( this was my punishment had to attend the court after 2 months for the case to get closed after paying a fine)and i pleaded guilty at court, paid court fees and the case got dismissed. I did not serve any community service.Then we relocated to India, i delivered a baby the same year in India. My husband and my kids are US citizens.I had just got my Greencard based on my husband's citizenship in 2010 Feb ,few days before i got arrested. But i didnt maintain the GC as i relocated to India the same year.Now we plan to move back to US in Jan 2011, before my re-entry permit gets expired in March 2011. But i am worried about 2 things below

1) would i NOT be allowed to enter US due to criminal record and be depoted back at POE?( in which case i need to fly back immediate flight with my kids?)
2) I plan to try to get naturalized after maintaing GC for 3 years, but will i get citizenship with criminal record?as the whole purpose of moving back with family to US is to get my citizenship?

Please advice.....