In universe Holdos plan is quite sound. The FO cannot overtake the Resistance fleet and a hidden Rebel base is nearby. Get there or as close as possible with the remaining fuel and evacuate the personal. Then have the FO follow an empty ship until its fuel runs out or if possible make a hyperspace jump as far as possible from Crait away.
Now this would imply that the FO fleet cannot just make a short hyperspace jump in front of the fleeing Resistance.
The problem is Holdo is does not appear to be a competent leader. (both to me as viewer and apparently Poe as character)
It appears that noone on the ship knew there was a planet nearby they were heading towards.
A good leader would have inform the whole crew about the evacuation as soon as possible both to ensure a speedy preparation of the evacuation and preparation of the landing on Crait (what to do when they land). And more importantly upholding morale.
The moment Poe gets mad (and accuses her of cowardice and treason) because the transports are being fueled she should have had him detained for clear insubordination.
Even after this display she is surprised when he and his fellow pilots mutiny. While the plan was already compromised at this point and telling him would be useless, she doesn't know this but didn't even attempt to explain her plain to stop the mutiny. Just "I hope you know what you are doing."
And once Leia is back she tells Leia "He is trouble, but I like him."
Another problem is Rose.
There were three desertion attempts which she stopped. Did the higher ups know about this and did nothing? Or did Rose keep those attempts hidden?
If the higher ups knew about desertion attempts they should have revealed at least part of the plan to raise morale.
If Rose hid those attempts she made a bad situation worse.
About the whole chase plot.
Out of universe the chase plot line makes no sense to me. The only time fuel was a problem was during an episode of Rebels when Phoenix Squadron had to steal fuel for the carrier IIRC.
Leias Resistance wasn't a hidden illegal guerilla force. (at least I never got the feeling it was supposed to be more like a has-been general playing doomsday-prepper) Fuel should not have been an issue after a single jump or those ships are the worst gas-guzzlers I have heard of.
Now if they had taken nBSG as template and made the Resistance jump to hyperspace at very short intervals and mentioned that the engines aren't made to sustain this it would have felt better to me. Maybe ad a line of "We can't lead a fleet of this size to any system. There are no defense fleets that could stand against it." would have made it clear why they have to jump to empty space.
Or it would have allowed for them to jump to different possible allies just to encounter other FO fleets already entangled with the defense fleets present, forcing them to leave.
IIRC the First Order isn't supposed to be the Imperial Remnant but a part of the Imperial fleet that fled into the Unknown Regions after defeat at Jakku.
Wouldn't it be funny if the Imperial Remnant become the "good guys" in Episode IX? And while reformed and not as terrible as the old Empire they are not doing it out of the goodness of their heart but to finally crush the rebellion and this upstart First Order. And the Resistance is forced to join them because the new Rebuplic is just as corrupt as the old Republic and the Empire was.