Hmm... In one sentence you acknowledge that all four use the same syntactic pattern; in another you that each context selects a different "grammar." I can only make sense of this if you reject a division of "grammar" into syntax and other components.
I would have used the term 'grammar' for syntax and morphology, but not semantics (hence my use of quotes in the para above). But perhaps that's just a question of terminology. My point is that the problem becomes more tractable if you divide it up, and recognize that syntax can be handled separately--and because the syntax of all four examples is the same, the syntax becomes simpler. Of course, Chomsky argued for that division a long time ago...
Another way of looking at the need to divide up the problem: if Tom's support to his daughter consisted of stacking up $10k worth of coins, and letting her lean on them, then the analysis (in your terms, the "grammar") of the second sentence would become more like that of the first. But I fail to see that as a change in the *grammar*.
CASL/ U MD