Honestly it doesn't look good for you. The burglary is considered a serious felony and yes you could face removal for this conviction. Only one would be counted because both crimes arose out of a single act. The look at the most serious.
I wish I could say this would be overlooked and it may be for awhile but when you go to renew your card, you have to have biometrics done and it will show your criminal history when the FBI does the check. At that time you could be referred to ICE and issued a notice to appear before an immigration judge.
There is what is called cancellation of removal but it requires a showing of good moral character, in addition to having 10 years of physical presence. You also have to prove extreme hardship to a "qualifying relative" which is a US citizen spouse or child.
If you are removed and are married to a US citizen you could apply again for resident status but you would have to request a waiver of your inadmissibility from the removal and the criminal conviction within in 10 or 15 rears of applying to be admitted again.
This is definitely something you want to retain an immigration attorney locally to review and to have them then contact your criminal lawyer to discuss. Your criminal lawyer is supposed to advise you of your immigration consequences but often they are clueless about immigration laws. Don't count on them protecting you from immigration consequences and get a local immigration lawyer to discuss outcomes with them.
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In the future, you may begin your questions with “FOR JUDITH” and I will be your personal immigration expert.