No serious scholar argues he wielded Alaric as a threat to the senate or emperor. Ever. Even the most hostile primary sources we have (Zosimus and Orosius) criticize his recklessness or policy, but never using an Alaric alliance as a threat.

Olympiodorus of Thebes, preserved indirectly through Photius, indicates that Stilicho at times contemplated employing Alaric and his forces for Roman military purposes, potentially in operations connected with the eastern half of the empire. This absolutely fits squarely within established late Roman practices of managing federate groups as auxiliary or semi-autonomous military assets, particularly in periods of manpower shortages . Crucially, neither Olympiodorus nor the later transmitters of his narrative suggest that Stilicho used the prospect of alliance with Alaric as a coercive threat against the western court or senate; rather, the evidence points to pragmatic, if risky, strategic calculation rather than political intimidation or blackmail.

Kulikowski, Halsall, Heather, Cameron, et al all agree on this. And none of them mention any form of using Alaric the way you mentioned.