Property ownership does not provide additional advantages based on the facts as you have recounted them. However, you are able to get tourist visas that allows you multiple US entries with a maximum period of stay for 6 months at each entry. Obtaining a B-2 tourist visas in your situation is possible upon showing that you do not have an immigrant intent; that at the end of each visit, you will return to your country of usual abode and where you have such firm roots that you do not intend to abandon. If you are from one of the designated :Visa Waiver Program "VWP" countries, you do not need a visa and you can come to the US for a maximum of 90 days and to return. If so, a VWP entry may also be a viable option and you can come to the US for 90 days on each occasion each such entry spaced a few weeks or months apart. Finally, when your LPR son becomes a US citizen, he can file an I-130 petition for you to become a green card holder yourself and with which, you can enter and depart the US as you see fit subject of course to some conditions. There are pros and cons for each of the options listed above and you are best advised to consult with an experienced immigration attorney who, hopefully can carefully discuss with you all of your options and alternatives.
Answered on Jun 06th, 2013 at 11:47 PM