Lucie--it's entirely possible she hasn't had a chance to read it yet or had to go back over it to get her thoughts together, or even that she's at a conference or just had a ridiculous crisis at work and has to sort that out first. It's not necessarily a bad thing.
My agent is known for his ridiculously fast responses. I know that I can't say this is true in every case, but I did an R&R for him. Most people hear back on fulls within two weeks, and I didn't hear back for two months. I just knew it was because he hated the revision and hadn't gotten around to sending out the rejection yet.
I found out later from a blog post that he'd had a couple of manuscripts he wanted to sign on, but they came at the same time so he gave each of them another read to make sure he wanted to take them. When I got the email from him, I was so certain that he was just sending a polite rejection that I had to read it a couple of times to see that he really was asking for a phone call instead.
So a little extra time isn't always a bad thing. There is probably a perfectly valid reason that isn't "I hate this book."
Zelenka--It sucks to have family not be supportive. Mine has always been oddly supportive. On the one hand, they encouraged me, on the other, I'd get questions about whether or not I was crazy because I talked about my characters like they were real people, or telling me that I needed to not focus on writing and worry about getting "a real job."
The fact is, though, that if this is something you want to do, you'll never know if you could have accomplished it if you don't try. Maybe your family doesn't see it, but this isn't a field about talent. It's a field based in learning and study and research and improving. Personally, I'd rather work my ass off to try something even if I know the odds are long because then I know I tried. Otherwise, I'd spend my life wondering if I could have done it, and really that's a regret I don't want to have.
You have us here to be supportive when you need it. Do what you need to do. Your family is trying to think of what's best for you, but in this case, they don't know the answer. You do. You're an adult and it's your choice to make. And you know you have people to support you.