Sorry, can't really help. We replaced all our blinds with cordless cellular shades.
If you crane your neck (yeah, I know, hurts to even contemplate) you should be able to see the holders that the blinds snap into. All the blinds I've ever seen in RVs have holders that are screwed to the underside of the valance and you just need to remove the blind to locate the screws.
Maybe a good cleaning will improve the performance , but new mini-blinds are very inexpensive. Lowe's and HD will cut to size for you. It's the cords that are binding- I'm not sure lubrication would help.
An attractive substitute for the original plastic tie-down is little stainless or brass cleats like these