You could be experiencing a couple of unrelated problems. The shimmy upon braking is usually a rotor thing. A shimmy at 120 KPH is likely a tire balance problem. Firstly, I'd work on the balance issue. Rotate the tires front to back & see if there's any difference. If there is, get all four tires rebalanced. If there's still a shimmy, perhaps you've got a bent rim. A decent tire (tyre) store should be able to diagnose everything at a reasonable cost.
Ron.
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Good s**t happened.  69 was worth the wait.
'92 stock semi-pristine ebony - 160K
'96 Grand Caravan - 240K
'01 Miata SE - 79K
'07 Chrysler Pacifica - 60k - future money pit.
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