Can I use a full-time offer to leverage a full-time position from another company instead of an internship?

Sorry if the title is confusing.. Basically, I'm a senior in engineering school and I'm pursuing a career in the energy industry, which I've been working part-time in for a few years. I got an internship offer from a company with the potential for full-time.

Now, this company does exactly what I want to do and they're located in the city I want to be in. But I can't take an internship because pay will definitely not be enough, and if I move to said city and they cut my internship I'll be screwed for housing, as it's an expensive city. I also won't get any benefits for a few months which is not ideal.

On the other hand, I was offered a full-time position in a totally different industry and a location that is cool but kind of "meh" to me. It pays quite well though. The position does catch my interest and I would have no problems accepting it as a last-resort, it's just not what I want to do career-wise at the moment.

So my question is, can I use my full-time offer to try to get the first company to rethink their internship offer and possibly extend me a full-time position? How would I go about doing this? I'm supposed to have a phone screen with their HR department Friday to nail-down the internship details. Should I email them before and ask or should I ask on the phone?

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