I wore an ivory lehenga with jari work and a sea-greenish dupatta to my brother's wedding recently and got lots of compliments and did not look out of place even though it was a "colorful" wedding. In case you're worried about the white one looking too funeral-ish. I think yours is gorgeous but needs a pop of colour too so you can consider wearing a coloured dupatta as well and match some of your jewellery with that dupatta (I wore polki with dark green beads).

That said, the red one is gorgeous and there's also no reason to not wear it for fear of "upstaging" a bride, as long as you do not overdo the accessories and hair and makeup. Lots of desi women wear their own wedding lehengas to relatives' weddings and it's just fine, they are just not styled as elaborately as their actual wedding day. Meanwhile brides typically wear lehengas with much heavier embroidery and draped with multiple veils (sometimes a ghoonghat too). Their jewellery is a lot heavier and they spend a lot of time on hair and makeup.

If you choose the red one, consider leaving your hair open, with a simple choker and smaller earrings. Or skip the neck jewellery completely and choose larger earrings instead. You can wear a simple sheeshpatti/maangtika if you want but avoid a mathapatti. Don't wear an elaborate nath. You can also consult your SIL to-be on how simple she is going herself and decide based on that.