You have a dominican girlfriend and child ?....... well if you really want to stay, just get married ( or prove you have been togother for 2+ years ).
You dont need anything to qualify....well apart from a passport, and no legal problems.
You dont need any proof of economical solvency, no dominican garantees, no job, no income, no titles or deeds, ........ nothing at all really.
What exactly will getting married to a Dominican woman (or proving they were together for at least 2 years) do for him? Perhaps being married will allow for residency to be applied for within the DR and without a need for a guarantor. That might be the case.
A girlfriend you lived with for more than 2 years does not ring a bell as counting for anything in this kind of situation.
I have been married for over 13 years, had residency starting in 2002, renewed at every renewal, and just recently was screwed by Migracion and am still going through my own special type of "regularization" based upon corruption, incompetence and/or they wanted more money from me at Migracion. I will only know in May, 2019 if all I submitted is good. Six months just to wait for them to print my residency card again. By the way, despite my marriage for many years to a Dominican woman, I still had to provide a proof of economic solvency to Migracion just to get back in the system (along with an apostilled/translated/notorized,etc,etc,... birth certificate and some other forms that needed filling.)