Yes, if you can prove the property is not solely owned by you then that will help it.
Yours is going to be a very tricky case, probably more than a usual high street solicitor would handle so I think finding the right legal team will be crucial. How would he fund a court case? Often solicitors will bill from any award so if he has provided them with details of the trust they maybe several steps ahead and feel confident of getting their fees paid.
The law looks at needs and fairness for asset split. On one hand it could be argued his needs are being met, if he has secure housing, pension etc however equality is an important test and he may argue that you had the assets at the time of the original divorce so should always had a share. Had a consent order been in place at the first divorce he could argue he would have had a share when it matured, irrespective of 2nd marriage.
The fairness argument is you have a 400k property whilst he is penniless. His behaviour won't be a factor since it's "marriage" which means you accepted this behaviour for most of the marriage.
Finances were not severed as no consent order and your legal team will have to argue that this trust was not an asset at the time of the first divorce which arguably it was, albeit time restricted.
Judges don't make settlements on moral fairness, it is simply about the law. This is hard something to get your head around.
Might be worth asking on this site or others for recommendations for solicitors or barristers as often a "barrister view" is worth hearing before deciding if court worth pursuing.
From your side, it probadly is, if he was asking for 50k, maybe not. But 300k is too much to just give away..just have to realise you could lose 300k plus 25k in court costs each. What do you think he is trying to achieve? Does he want enough to buy a house? If so would your children inherit anyway so might feel less of a bitter pill to swallow.