"We had a good party but we had wet weather too."
Translation:Gaethon ni barti da ond gaethon ni dywydd gwlyb hefyd.
parti has caught the 'object of a conjugated verb' mutation and does not pass it on.
If we were describing a chair (cadair), say, then any adjectives following the feminine noun cadair would all mutate:
- Roeddwn i'n hoffi y gadair goch fawr oedd yn y 'stafell 'na. (I used to like the big red chair that was in that room.)
Your dywydd is a lenited tywydd, so the rule does apply -- it is lenited just as parti was to barti.
(And it's tywydd gwlyb rather than tywydd wleb since tywydd is masculine - at least according to the Bangor and Trinity St David dictionaries. GPC has it as either masculine or feminine.)