RF 16 mm f/2.8 or 35 mm f/1.8 for EOS RP user ?

For my EOS R (i.e. without IBIS), I have an EF 35mm f/2 with OIS and - now since 3 weeks - the RF 16mm f/2.8.

The 35mm is a great, solid tool for many purposes. Town, street, indoor, landscape, public and family events and so on. IQ is pretty fine and OIS is solid. It's my most frequently used prime lens.
If you do a lot of indoor shooting (without flash ?), the fast aperture and the IS is helpfull.
And yes, 35mm f/1.8 is a big difference to the 35mm just covered by your kit zoom lens.

The 16mm is a complete different thing from my point of view. For me, I wouldn't consider to use this lens for indoor family photography - but that's my personal view. (I don't like UWA portraits ...). It might be different if the shot should cover a dozen people around a table in the living room...
It's great for any purpose where ultra wide makes sense. However, as just mentioned above by another forum member, you will have to go through some learning curve concerning the composition of your photo. A lot of fun - so never stop learning in our life.

If you are planning to take the 16mm indoors - without a tripod, maybe without a flash (I don't like flashes during family events), maybe in some cozy but not too bright lighting - then you should think about the fact that the RF 16mm has no OIS (and your RP has no IBIS).
I like taking shots in the interior of churches or museums (without tripod) and here it was important for me to find out which shutter speed is my personal handheld limit. Not just having the 16mm, I took the 24-105mm, switched off the OIS and took shots at 24mm with decreasing shutter speed. What's still ok for 24mm should give you an acceptable keeper rate at 16mm.
So living people require a faster shutter speed than a statue in a church - for the price of a higher ISO.
If you look to ISO, the difference between the 16mm and the 35mm could be somewhere in a ratio of ISO 200/3200 (wide open, max. handheld exposure time).
(I made this section a bit more detailed because having no IS at all for indoors is - for me - more challenging the being outside ...)

With 16mm, the effect of abberant lines can become much more distinct compared to 35mm. If you can crop that out of your photo or if you have a good post processing tool, it should be ok, but it's worth to think about that effect.

I didn't feel that - for me - the 16mm is a fine 'all day walk around' lens. But it's small and got its place in my bag.

My - very personal - feeling would be that the 35mm could be a fine lens for you.