"But what if the parent hates and refuses traditional Catholic priests, wants Novus Ordo "sacraments" (such as receiving "communion" from a woman or other abominations), and has a Novus Ordo funeral. Is a child obliged to attend such a funeral?"
We are never obliged to offend God, not for anyone, not even for our parents - and for me, that's what I would be doing if I attend a NO abomination for any reason.
I can only imagine being in the situation the OP is in. All I keep coming up with is, I would walk out before the service starts, or not enter the NO church at all until after the service is completely and totally over. That is the only true way to not participate.
About 20 years ago, the one time I attended a NO funeral service, it was for a young man I worked with who died suddenly - to this day I regret ever "going but not participating" to that complete blasphemous, mockery of the True Mass. I'll never do that again! It really about made me throw up to see what goes on at one of those things. It is no wonder this world is in such a mess. I will never in my life ever do that again, not ever again no matter who dies - and I recommend that others do the same - just stay out.