****. I want to help you but from this post alone I can see tonnes of issues. Internally and externally.
I'll be brutally honest for your own good, you can take my advice or leave it though, that's up to you.
- "I really like this girl we've went out twice." It's ok to really like someone. But it also depends on why you really like a person. If the reason is because she's cute, and willing to go on dates with you and you don't have other girls in your life. Then that is the wrong reason to really like her, but you will get feelings of course. This is a dangerous position to be in because you will be very needy and she will be repulsed by your behaviours. You should be coming from a place of security. You should have several cute girls that like you. And one or two of those girls that demonstrate qualities you like, those are the ones you should really like.
"I'm new to the dating scene due to some personal problems in my life." Hopefully you have fixed those problems. Girls GENERALLY don't want to be with a guy that can't take care of himself. They want to lean on the guy not the other way around. Also girls subconsciously like guys with experience and confidence with other girls. They won't like that on the surface though, but deep down they do. So start dating more girls especially if you really like this girl.
"I am shy and tentative and I want to be interesting to her. " Horrible mindset. You can be shy, I'm not going to bash you for that. But first I will advise to get rid of your shyness. YOU ARE NOT SHY. You have impemented shy behaviours for a long time so that you believe you are shy. You are not. SHyness can be destroyed with anyone. You just have to work really hard. But for now it's ok to be shy as long as you can explain to people and girl you like that you are shy. That shows some vulnerablitiy and that is attractive. Hiding your shyness or trying to look confident whne you're not is NOT attractive. And trying to impress a girl is the worst thing you can do. The best way to impress a girl is not to try to impress her. Simply talk to her find out about her, kiss her and the fact that you are not trying to impress her is impressive in itself. Every guy tries to impress girls with flowers, chocolates etc. it just looks needy and wimpy, and loses all attraction. DON"T do that. No matter what girls say. They do not respond well to that for a guy they just met.
"Both times we went out her friends and family were there and I didn't want to say or do anything that gave off the wrong idea so I kind of just sat there." If her friends and family were there. It wasn't a date. You would just be a friend in this situation. Take her on a PROPER date. Which means you must be alone with her. You could grab milkshakes, go to the beach, watch a movie. But you two must be alone or it's not a date. If she says no to that. Then good you were at least rejected properly. What you're doing now is just being her friend which is worse than a rejection. Because it's not genuine.
" I didn't want to say or do anything that gave off the wrong idea so I kind of just sat there."
Doing this makes you less attractive. This WILL give off the wrong idea. Talking about retarded, or rude subjects will make her more attracted to you than doing this. Speak your mind, say random things, piss her off if you have to. That will make her attracted. Saying nothing and being awkward ruins it. STOP trying to impress her, be yourself. Shyness is not yourself! Shyness is hiding your true self. You true self would be the one that speaks all the thoughts going n in your head. So do that. Even if it's risky. If you think about wanting to kiss her. Tell her that! Say "I was just thinking about the end of the date if I will have the courage to kiss you." Risk awkwardness for attraction.
All that should be applied for any girl you like. But the main issue I see here is you are putting her onto a pedestal. YOu are making her out to be a special prize. Stop doing that She's just a girl that you like and you'll like many more girls. So get properly rejected or receiprocated. But don't beat around the bush, stay quiet and try and impress her by not saying anything. All these things are clearly ruining it. So fix yourself now!
1. Get over shyness
2. Stop filtering your mind, and speak every awkward/risky thought you have.
3. Date more girls.
4. Go on PROPER dates alone with the girl
5. Stop putting her on a pedestal
6. Stop trying to impress her and just be normal and real with her.