I have a very accepting family, and friends. In all honesty I've come across very little adversity in my transition, and very little bullying ect. growing up due to being different. I guess I'm just saying that to make clear that you should take what I'm saying with a grain of salt.
I didn't expect anyone to recognize me as male before I outwardly appeared as male. I didn't even expect male pronouns after top surgery (which was ~8 months before T for me). I didn't ask, so them not doing it didn't make me feel bad. Not everyone has this option mentally or financially (to deal with getting T as quickly as possible). When I started hormones I told everyone what I was doing. I never said "use male pronouns" or anything. Eventually people just started to.
I think a lot of times its hard for people to change what they expect, or what they are used to over the past 17-18 years (I'm assuming in your case). For me it was ~21/22. A lot of people don't have the time/capacity to think that much before they speak, or move to open your door, or let you order first. Its just what they've always done. Habits are hard to break. It could be that your family truly is accepting, but just are having a hard time breaking habits. (I really can't say, but you didn't describe anything that really stands out to me as distinctly non-acceptance). Maybe its also your age. I hate to say it, but many people are apt to see anything like this before graduating high school as potentially "just a phase." Not saying its at all right, but its there.
My father still refers to my sister and I as "the girls." He is 100% completely accepting and supportive. In fact, I think he has been more adamant about the necessity of some of the steps than my mom (who is the most supportive mother anyone could ask for ). He always waits for us to order first (unless someone needs more time to think). Its just his habits. I don't take offense. [also if there are four of you and your mom goes, and then your sister, and then you and then your dad... its still women first men second. I wouldn't be so intent on going last, maybe just try follow your dad's example and let your mom and sister go first.] I think sometimes we as trans people get so caught up in our heads that we sometimes don't realize that our gender isn't at the center of other people's minds.
As for the relatives... Is your grandmother aware of your situation? If not you can't so much blame her. I was getting flowery "granddaughter" cards from my grandpa for years until my mom told him I was transitioning. I went to his 90th birthday party that year, and he was lovely and accepting. Maybe your parents haven't taken the time to let her in on it. You may have to do that deed yourself. Maybe try to deal with your extended family differently. If they go in for a hug respond with a "man hug" as you call it, or try making it there first for a handshake. I don't know.. I don't really see my extended family much.... I guess I hug my aunt but my cousins (one male one female) I usually just wave hello or goodbye.
Sometimes in being trans acceptance is slow coming, and oftentimes it comes first in the form of them not yelling at you, or trying to convince you otherwise, or not letting you leave the house looking at all boyish, or monitoring your internet usage ect... These may seem like small things, but just as Nikko said... In time they may come around. Its not like they're shoving the bible down your throat and telling you you'll go to hell, or that you're dead to them.