How to tell partner I'm not comfortable with baby bathing at his mom's house?

I (23 F) am currently pregnant with my partner's (23 M) baby. His mom is amazing, and she is so excited for her first grandchild. She is super willing to watch the baby when they're born.

I am all for it, but I do have one hang up, which is over her tub. Our baby won't be bathing in the tub for a while, but they of course will eventually. I do not want my baby taking baths in his mom's tub. The tub has a lot of brown streaks, the caulk is messed up (and potentially molding), and it looks terrible and very unsanitary. I've tried in the past to kindly hint that my dad could go over there and at least fix the caulk in the tub, to which my partner has declined. I am worried how it might come across if I tell him I don't want our baby bathing there, especially if he tells her (which I don't think he would).

Is there a way to politely communicate this now?