I'm sorry your family isn't more supportive. Maybe the real issue is that you should talk to them about how they should support you with what you're doing now instead of making you feel inadequate.

There's absolutely no way you could transfer anywhere but down.

Have you calculated where all As this semester would put your GPA? It might not even be possible to go from below median first semester ---> top 10% second semester.

However, you said you're on a full scholarship so your situation really isn't that bad.

I hear Cooley is nice this time of year...

But seriously, get all A's and A+'s and write one hell of an addendum explaining your situation for fall (and I mean that it better be crazily unique and demonstrate a ridiculous burden on you...like your entire family was kidnapped and you had to rescue them single-handedly using the training the CIA gave you before they discharged you for being too much of a badass).
Also, depends on your schools curve.

I did…and it doesn't seem like it would still be enough. But if I got all As (or As/A-s) this semester, would a school take into consideration the jump in GPA from fall to spring, given the circumstances I had in fall, or is it really only the overall ranking that matters?

I´m really sorry about your situation. It sounds rough, and like you're not getting much support. Please remember the title you gave this thread, though..."should I even bother?" I assume you were referring to trying to transfer. The overwhelming response here (actually, I think it's unanimous) is that the answer is no. Just no. Several people have pointed out you won't be able to transfer at all into a better situation than the one you're in now.

It seems like your parents are disappointed in you, pressuring you, etc. I understand your desire to please them, but at some point, everyone just has to be reasonable and accept that facts are facts. Have you thoroughly explained the situation to your old man? Something along the lines of, "Dad, I know you would like for me to be in a better school, but that's just not going to happen. For whatever reason, my grades aren't good enough to transfer into a more prestigious school that would give me any tangible benefit, and at best I'd end up losing my scholarship and paying a ton of dough to end up more or less in the same situation I'm going to end up anyway. Sorry if you're disappointed, but the logical choice is to stay put and make the best of it."

Good luck, in any case.