Interestingly the situation is the same here in Welsh and English. 'Must' and 'have got to' are usually interchangeable when it is about obligation (ditto rhaid and gorfod in Welsh), but ONLY 'must' is allowed when it's about supposition (and only rhaid in Welsh). So:
She must go = She's got to go
Rhaid iddi fynd = Mae hi'n gorfod mynd
She must be late - (NOT: She's got to be late)
Rhaid bod hi'n hwyr - (NOT: Mae hi'n gorfod bod yn hwyr)
And note the different construction with rhaid in the two types: obligation uses i, supposition uses a 'that' clause.
351 in the Grammar!