Hilda and Connie look like sisters—they both have the "same rather golden, glowing skin, and soft brown hair, and naturally strong, warm physique" (7.66), but the similarity ends there. Hilda may look "soft and warm […] as a ripe pear" (7.70), but she's strong-minded and unwomanly with "the very hell of a will of her own" (16.116).
It doesn't do her much good. When she goes with Connie to Venice, she spends all day "drugged" with the sun, jazz music, and cocktails, enjoying the men "waiting to plaster some woman's stomach against their own" (16.159) without actually having to have sex. Which, by the way, she's totally happy to be done with, since men are "nasty, selfish little horrors" (16.159) when it comes to that.
See, underneath the socialism and the unconventional upbringing, Hilda is just boring and conventional. As she says, "she may be on their [the working classes'] side in a political crisis, but being on their side makes me know how impossible it is to mix one's life with theirs" (16.184). She objects to Connie's relationship with Mellors because "being solid Scotch middle class, she loathed any 'lowering' of oneself or the family" (16.132-33). Hilda's whole motivation is wrapped up in two goals: get her own way, and keep the family dignity up.
Not very inspiring.