You don't *need* to stand. Really. It's possible to get up even very steep hills without standing to pedal. (I can remember doing it, just don't have the muscles now...)

The way I learned to stand and pedal was *first* I got comfy enough on the bike that I could handle turns with my hips. Then I learned to hold a line with my hips. Then I learned to ride with no hands. After I got those balance skills down, I was a lot more likely to stand and pedal. Every bike I've had, I've needed to relearn the balance skills some. Each bike handles a bit differently. The right movements on the Huffy kids bike I had in the 80s are not the same as the right movements on my modern mountain bike . Heck, I'm still not comfy riding with no hands on my current bike.

It sounds like you're uncomfortable with a whole slew of balance skills. So give yourself a break on the standing, and work on something that feels easier. Don't beat yourself up, just work on little things. Balance skills all work together, and the more little ones you have that you do right automatically, the more the big things will come together.