What can be done if my brother has been getting into the house of which I am the trustee and have taken all of the assets without logging them?

Change the locks, send him a bill for the new locks, tell him he must return all the items as legally you are responsible that the assets remain in the Trust and by law, so that you personally do not have to pay for what he took, you would be obligated to report him to the police for theft, and civilly sue him, along with reducing by a like value whatever he has taken from what ever he is eventually supposed to get from the Trust. That your minor daughter, when she reaches 18, will be very upset that he stole from her and will be entitled to sue him, using a high estimate of the value of the assets taken plus interest at 7%. He knows what he is doing is entirely wrong and I am sure you have told him several times, so the only way to stop him is to take harsh action. When there has been a death of one's parents one or more children often try to take advantage of the nice kid in the family. Unfortunately, I know from personal experience. If you are not harsh, he will keep doing this and your daughter will get mad at you and it is making her life harder than it should be. I suspect you will actually have to file suit [there are forms from the court and on the web you can use it is relatively simple and you may not need an attorney, but if you sue for conversion you could claim attorney fees although the one time I did the judge rejected that but did award my client a nice sum for the trouble caused her]. Good luck.

You as trustee have the duty to call the police and file a police report regarding the theft.

That is theft and should be reported to the police.