Embedding Sets of Sets
Python 3, 84 62 58 bytes

Recursive function, A is a list of sets and B is a frozenset; returns false if \$A\preceq B\$ and true otherwise.

f=lambda A,B:A and all(A[0]-b or f(A[1:],B-{b})for b in B)


@PoonLevi and @SurculoseSputum helped save a great amount of bytes.

Explanation:

If A and B satisfy the relationship described, then this recursive statement makes sense:

The first set in A is contained in some i-th element of B and A', B' also satisfy the relationship, where
A' is A without the first set
B' is B without the said i-th element


Because I am returning the reverse, I am actually ensuring that, if the first element of A is contained in some element of B, then A' and B' cannot satisfy the relationship.

Try it online!