Cross-database queries are slow
I looked at your plans and found the cause of this difference: 

you get a slow plan in the database with compatibility level 100 (see the plan: CardinalityEstimationModelVersion="70" i.e. the old cardinality estimator is used). 

Your good plan is generated using new cardinality estimator of SQL Server 2014: CardinalityEstimationModelVersion="120"

You should update your question with the view text to find out the exact predicate where estimation goes wrong, but in your slow plan cardinality there is underestimation of the join with OMInternalOrganization so NL was chosen while in the fast plan you see Hash Join for this table, starting with this join slow plan shows many other Nested Loops while Hash Join is better and it's used in fast plan.

I don't know for what reason that database was left in compatibility level 100, maybe other queries perform better with old cardinality estimator, so instead of global changing compatibility level to 120 for that database I suggest you to use local query option: OPTION (QUERYTRACEON 2312) to forse your query to use new cardinality estimator even in that "old-style" database.

More on cardinality estimator here: Cardinality Estimation (SQL Server)

And here: Optimizing Your Query Plans with the SQL Server 2014 Cardinality Estimator