My attorney did not cover some of the important topics in our case, and the decision was shocking. My 2 daughters and I, lost in a huge way, at the custody hearing. I am wondering, what, if anything, I can do to get a new trial, and avoid paying the rest of my attorney fees, because I feel my attorney blew an easy case?

First of all how long ago was this? Second you can in some states contest the hearing decision if within a certain time frame otherwise you have to start all over or file an appeal (which can be expensive). Depending on the Motion to the Court by which party your attorney should have asked for attorney's fees. If you brought the action and won you would have gotten attorney's fees for bringing the action and winning. What was the reason your attorney did not bring up the important issues you speak of? Did you meet and discuss these topics fully prior to the hearing and he agreed to bring them up?

First I will say this, going in, only one side can win, but often both sides think they lose in many family court hearings. Going in, both sides have attorneys that tell them, don't worry we will win for sure ( well it happens for to often, seldom does an attorney say I will try but I doubt we will win. And if you were there, why did you not ask or tell your attoreny to address some of those issues?

And also the questions twinkie asked are valid also.

But at this point, it is up to your state ( if in the US) or your local laws as to appearing or asking for a new hearing. As for as paying the attorney, this is why most attorneys want to be paid up front, since if you lose you never want to pay them. You can ask in some states for a mediation of the attoreny billing if you believe it is improper, and ask the attorney for a credit for not doing certain things ( not saying they will do it, but you have to ask first)

In the end, it will depend on the law as to what you are allowed and as to what level hearing this was and if apeals are allowed at this point.

I have been noticing more and more that many lawyers seem incompetent
They seem to be not covering main issues almost like they are on the other side.
Then the police, child services and others even lie in court and if you get a chance to ask them why they lied
They say "We are allowed to!" While your lawyer just sits there.
Unfortunately, it doesn't seem like there is anything you can do about the injustice in the justice system.

My attorney did not cover some of the important topics in our case, and the decision was shocking. My 2 daughters and I, lost in a huge way, at the custody hearing. I am wondering, what, if anything, I can do to get a new trial, and avoid paying the rest of my attorney fees, because I feel my attorney blew an easy case?
Just curious: what were you expecting to happen at the hearing? And what did happen? And, why do you say your attorney "blew an easy case?"