I am sorry for your loss.
You need to contact the brokerage firm(s) for a definitive answer with respect to the 1099s.
However, you would report dividends earned prior to your father's passing on his 1040 using his social security number (if a return is required to be filed).
Dividends earned thereafter (in the trust) would be reported on a 1041 with K-1s issued to the (primary) beneficiaries named in the trust.
