First off, this isn't a "relocation" issue. This is plain firing.

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sold the company to a different enterprise
Different employer means that you were fired from the job that you had. At worst, it's a "refusal of work" if you don't work for the new company, and a three hour drive to work is "too far" and renders it unsuitable.

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I am currently 16 weeks pregnant, I'm not sure if that matters or not,
It matters in the sense that it makes things worse for you. It raises "able and available" issues. Do NOT ever talk about your pregnancy or use it as an excuse when it comes to UI. UI is no sympathy system. You must lose your job for the right reason, be able and available for work, and looking for work. If you want to say, "I can't do that because I'm pregnant," you won't see any UI money until you can do what is required.

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Would I be eligible for unemployment if I voluntarily quit my job due to an unwillingness to relocate?
If you "quit," you'll complicate things for yourself. You keep doing the job you have right now exactly where it's at, and when the employer says, "starting tomorrow, you won't be working here, but if you still want work report to Tampa." At that point, you stop going to work because you were fired from the job that you HAD.

Don't throw around the word "quit" ever again. It will just confuse people.

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Additionally, would my eligibility change if my (new) employer offered to fund my relocation?
No. Too far is too far. However, it might not even be a "refusal." If the employer is requiring you to reapply for the job, and you chose not to, that's just fine. No one can make you apply for a job except the UI people. In this scenario, there is no "refusal" because you were never made an offer. An offer is NOT an invitation to apply with a high probability of being hired. It looks like this "Starting Monday, we want you to work as a data entry clerk. Your hours will be 8 am to 5 pm. You'll work Monday to Friday. Do you want the job?" If they say things like "you'll have to apply," or "the job is contingent on you passing a drug test and background check," then that's no offer.

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Would any other factors affect my eligibility?
Yeah, if you use your pregnancy as an excuse to not to do what everyone else has to do, it will be a problem.