There's a lot of factors involved in whether a tooth can accept a post and crown. Some of these are a judgement call, but there are some specific standards involving the amount and shape of the remaining healthy tooth matter. If there isn't enough healthy tooth, or if the edges of the tooth are decayed irregularly so that a good margin can't be prepared, the tooth might not be a good candidate for a crown.
Everyone's teeth are different, and mostly in ways that you and I can't see. A dentist with an x-ray can tell a whole lot more.
As with any medical work, you're entitled to ask questions of your dentist, such as why she doesn't think your teeth can accept a crown. If you want to get a second opinion, you should definitely do so, but understanding how your first dentist is thinking will help you either way. You should also try to gauge their level of confidence. One dentist's "yes" and the other one's "no" might both mean "I think I can pull that off, if everything goes right."
As for the other teeth that are bothering you, make sure you're speaking up and telling the dentist what your concerns are. YOU are in control and the dentist should respect your concerns, and in any case, a tooth that is causing you pain should always be high priority. Now, the dentist might have good reason to feel your molars are a priority-- and she should tell you why. But you always have the final say in deciding what gets done and when.
I think most dentists are honest and well-intentioned, but the bottom line is you need to have a good relationship with your dentist, and you need to trust her opinion. If she seems to be focusing on something you don't want to work on right now, ask her if there's a reason that needs to be done before the teeth that are bothering you. If there's no good reason, or if she continues to ignore your requests, it may be time to find a dentist that's more on your wavelength. At the same time, don't assume the dentist is wrong or lying just because your daughter had a certain treatment and your treatment is different. Every tooth is different.