My mother created an irrevocable trust and left out on purpose some siblings. Can this secular legal trust be disqualified by a bais din or does bais din rule it is legal?
It is hard to give a definitive answer without out knowing how the trust was made, etc. In general though, although this is not a very advisable thing to do, but if the trust was done in a way that it is considered by torah law as if your mother gave her possessions away while she is still alive, then it would not be disqualified in bais din.
As a side point, see the following link, ESTATE PLANNING, WILLS, AND HALACHAH for kuntris that discusses this topic very clearly.