planning to petition the kids

[lho 0]

i'm currently living here in NC, been here for almost 4 yrs...already a LPR holder... my life is full of complications even upon starting my petition processing. 1st: i had my middle name wrong because of some clerical error. Instead of Nolasco the name appears on my BC is Lelasco... what i did, so just not to delayed the process i just used what is in the records which is the Lelasco. Because i was pregnant from my fiance that time and he want me to actually deliver in the U.S... 2nd prob: i had 2 other kids( from a 1st relationship) wherein i didn't include in any of the paperworks i did that time,not even let consular officer know i had other kids... because they had a falsificated BC, because my former bf that time wants the kids to get his name but we're not married and under the new family code babies born to an unwed parents has to keep the mom's name....and since i know that it will take a very long time and money before the prob gets straighten up... i just opt not to include them and planned to just save up some money and take care of it once i'm already here...Now they are 16 and 14... i wanted them so bad to be with me....

Question:

1. Can i still petition them even though they don't appear on any of my papers before?

2. Am i not going to be in trouble with the immigration because of lying about my kids?

i need help please give advice on what's best to do... i love my kids and i want them to be with me