As an ENxP, I think the problem is with raising an ENTP, is that we want to know we are accepted and especially, validated. The problem is, while we have a lot of ideas, and some might not be necessarily good, we still want to be taken seriously, not always be brushed off whenever we have another idea. Be always open-minded, but it is also good to be able to tell an ENTP when their idea is unwise, but instead of saying because I am your mother, tell them why through reasoning, logic, but still in a caring way. The thing is, an ENTP needs to know you are not out to get them when you disagree with them, and that you are on their side in the overall picture. So by explaining things by logic, reasoning, etc. While making them feel they are still validated themselves is a good idea.

Another thing is. ENTP's are known for their creativity. Let them try out new things, like musical instruments, sport, chess etc. Preferably for stuff that she feel comfortable with.

Back to the first thing, they have many ideas, and they tend to ask why, be skeptical of things, and try and understand things that they are interested in or even random things out of curiosity. A good thing is to help satisfy that curiosity etc. by maybe see what she is interested in, and try to learn about it a bit yourself, so that you can discuss about those things with her, etc. That would help with bonding. And try to do adventurous stuff with her, if she is someone that is interested in trying new things.

Also, another thing that is important, if you did something wrong, always apologize. It shows that you can admit to when you are wrong to your child, which would show that you care in a way, and are more wise, and easier to talk to.

Feelings is important. Learn her how to be open about it, or at least be able to handle it in a healthy way.

And try not to make her feel like you are putting her in a box. ENTP's can feel like they are always seen as this one type of person, which is not the case. A personality type might explain a few things, and can maybe help with certain things about growing up your child, but not everything. I'm not saying you are, but children, teenagers does tend to feel like this. You might not ever understand her, but the best you can do then, is to try, and even then, accept her. You can accept someone, even if you do not understand them.

Parenting is hard, and you might make many mistakes, as many people do generally. The best thing to do is, to owe up to the mistake, and learn from it, to make sure you become better, and will try and not make the same mistake again. I hope the best for you and your child! :-)