The bet would be that in the long run (talking 5-10 years down the road after the EU has built their defense), the EU would still be more likely to ally with the US than China.
The current administration perhaps thinks that alienating them in the short run is the only way to get them to actually get serious about building military.
The reason why the EU never "got serious" about building military after WW2 was mainly due to US interference.
The EU actually spends quite a lot in defense, but does so very inadequately. Each country has their own army, so there's a lot of overlap in spending. I actually think that now that the US is essentially an enemy nation, EU will be forced to integrate more, as that's the only way it can pose a meaningful response. That can only be a good thing.
Also, I think you are underestimating how much the US is alienating EU in this, and how badly it is damaging relations. Trust is something you earn in droplets but lose in buckets.
And his plan to achieve that is by pissing off EU? If anything Trump has done a great job to make EU look at China more favorably.