Doing a second doctorate to get back on a research track?
A second Ph.D. is generally a bad idea, as noted elsewhere in other answers.  

Instead, there are several other paths that you can pursue to get back into research, depending on your goals.  The main ones that I would think of are: getting a postdoc, joining a lab as research staff, or joining an industrial lab.  All of these will lead you back into research in some form or other, thought probably not your same line of research that you were working on in your Ph.D.

You've got a gap on your CV, but not an unusually large one, so I don't think that needs to be a major barrier.  More concerning is the fact that you don't seem to have a professional network: the thing that you want from your old advisor is not for them to hire you, but for them to connect you with other different professors or industrial folks who might be interested in hiring you.  Going to conferences in your field is another good opportunity for networking, but it will be more effective if you can get help from your advisor or other professors who you have gotten to know during your doctoral program.