Generating topological sequence from DAG with additional "not appearing before" constraints
Let's say the 2 nodes in question are node x and node y. If you want node x to not appear before node y, then, as Yuval Filmus mentioned in the comments, you want it to appear after y.
What does this mean?
If x is a predecessor of y, then the graph would not be valid, because by definition, a topological sort puts all predecessors before their childrens.
If x is not a predecessor of y, you could add an auxiliary edge from x to y. This ensures that x will definitely appear before y, again by definition of a topological sort.
Followup:
Adding an auxiliary edge may cause some problems, here are some possible solutions to resolve them
Shortest/longest path in weighted DAG: Just set the edge weight as 0
Shortest/longest path(number of edges used): Give all non-auxiliary edges value of 0, treat as SP/LP in weighted DAG