Most women don't haven enough testosterone to get really bulky unless they're using steroids or hormones, so you can lift weights without having to worry about looking manly. Circuit training would probably be good for your purposes. Most gyms have a bunch of machines lined up or in a circle and if you move from one to the next with little or no rest in between you can get some good strength training, burn a lot of calories and get in a good cardio workout all at once. Most gyms will have a personal trainer show you how to use the equipment when you sign up. If they do, take advantage of that but keep in mind that trainers are also salesmen, so if they try to sell you supplements, fat burners, diet pills, etc. don't fall for it. You don't really need them, whatever the trainer might say.
http://www.sport-fitness-advisor.com...-training.html
As for your mom and sister not talking to you, I'm actually kind of jealous. I think my life would improve if she'd let me be for a while. And if you go to them and try to make nice it just encourages this kind of behaviour. You should try not to let this bother you, and if it does you should try not to let them know it bothers you. If they know this is a big deal to you they will always be able use the silent treatment to manipulate you. Maybe you should plan on spending Christmas with Uncle Fred this year. And if your mom breaks down and offers to "forgive" you and invites you over for Christmas you can just tell her you appreciate the offer but you've already made other plans.