Mrs Weasley planned to pick things up second-hand.

She answers this question directly.

"That lot won't come cheap," said George, with a quick look at his parents. "Lockhart's books are really expensive..."
"Well, we'll manage," said Mrs Weasley, but she looked worried. "I expect we'll be able to pick up a lot of things second-hand."
_{(Chamber of Secrets, Chapter 4, At Flourish and Blotts).}

Since wands are a highly personalised item it's doubtful whether they could pick that up second-hand. But if they couldn't then it's quite possible, as Radhil says in the comments, that they could've used a cheaper wandmaker than Ollivander, who was the elite after all. Uniforms, pets and textbooks can all be bought second-hand on the cheap:

Mrs Weasley and Ginny were going to a second-hand robe shop.
_{(Chamber of Secrets, Chapter 4, At Flourish and Blotts).}

As it happened, Harry helped the Weasleys out considerably by donating the Lockhart books he'd been presented with in Flourish and Blotts to Ginny.

The crowd cheered and clapped and Harry found himself being presented with the entire works of Gilderoy Lockhart. Staggering slightly under their weight, he managed to make his way out of the limelight to the edge of the room, where Ginny was standing next to her new cauldron.
"You have these," Harry mumbled to her, tipping the books into the cauldron. "I'll buy my own -"
_{(Chamber of Secrets, Chapter 4, At Flourish and Blotts).}

This probably meant that Mr and Mrs Weasley had more money to spend on a wand.

Nevertheless, the fact that Mrs Weasley emptied her account of literally every coin indicates that money was very tight that year. It's possible that it wasn't quite as tight as the question suggests. Valorum's point that Mrs Weasley's earthly wealth may not have been in the vault is a good one. She probably brought whatever remained of the money she had extracted last time along and added to that money the one Galleon and several Sickles in her account.

What would they have done if they'd still not had enough for the wand and books? They would, as Mrs Weasley put it, "manage". In other words, they'd do what real life parents do when their children need essential items they aren't able to afford - scrimp and save, making personal economies and sacrifices if needbe for the sake of their family.