I've thought a lot about this, too. By my definition, not to be a Tommie downer, you aren't describing "support." I've decided based on my experience that there are three levels, from "sucks but isn't killing me," to real great. I'm not including outright rejection, since that's obvious.
"Tolerance" happens when someone tells me they have compassion for me and don't say they hate me and never want to see me again. But when I probe them with questions I find they are trans-phobic in general, but they don't direct that negative energy or speech toward me. Tolerance isn't much better than rejection, but it could be worse.
"Acceptance" happens when someone tells me "It's okay who you are. I still love you. I support you." Well, no, they aren't supporting me when they say "its okay" and use the word "still." They aren't supporting me when they start communicating with me less often.
"Support" is wanting to learn more about my experience, telling me they are going to call me by whatever name and pronoun I want to use, telling me their only worry is for my safety, and including me presenting as a trans woman in their activities. Out of all my family and friends, I have one brother, his wife and their grown children who actually support me. For example, they bought a ticket for me and asked me to tailgate with them at a college football game next Saturday. I will be a fully decked out, accessorized, A-cup bra wearing, fan girl.
It sounds like your dad is starting to come around though. Be patient and give everyone in your life some time to adjust. Sometimes it takes a long time, but it happens. Hoping things get better for you.