Watto didn't want to part with Anakin so I don't imagine it would have mattered what Qui-Gon had; he could have brought anything to Watto and it's unlikely that he would have accepted. Watto was willing to gamble Anakin only because he had a weighted set of dice. When Qui-gon used his powers to make it land on blue, Watto was mad but had to accept it.
Qui-Gon had a specific mission; Shmi wasn't part of that. Her presence would have interfered with Anakin's ability to remove himself from attachment, which was vital to his training, so while he opened with his haggle for both, and his morality might have made him give a half-hearted bid at her and promise Anakin he would have a go, he wasn't going to jeopardize the possibility of Anakin, his main mission, to get her.
He never really wanted Shmi, and Watto was never going to part with both... you never open with what you really want in a negotiation; Anakin was the goal. In the aftermath of the race, Anakin did ask about his mother, and Qui-Gon DID say he would try; but even if he had wanted to go back for Shmi, it's likely that Watto, with this loss to an 'outlander', would be all the more stubborn and hardened to withhold Shmi just to spite him.
QUI-GON : I'll wager my new racing pod against...say...the boy and his
WATTO : A Pod for slaves. I don't think so...well, perhaps.
Just one...the mother, maybe...the boy isn't for sale.
QUI-GON : The boy is small, he can't be worth much.
WATTO shakes his head.
QUI-GON : (Cont'd) For the fastest Pod ever built?!
WATTO shakes his head again.
QUI-GON : (Cont'd) Both, or no bet.
WATTO : No Pod's worth two
slaves...not by a long shot...one slave or nothing.
QUI-GON : The boy,then...
WATTO pulls out a small cube from his pocket.
WATTO : We'll let fate decide. Blue it's the boy, red his mother...
WATTO tosses the cube down. QUI-GON lifts his hand slightly; it turns blue. QUI-GON smiles. WATTO is angry.
WATTO : (Cont'd) You won the small toss, outlander, but you won't win the race, so...it makes little difference.
While his moral compass would allow him to flip the dice Watto rolled to get Anakin (which had been rigged anyway), he wouldn't use it for 'side' activities on side parties; those not directly in his path. He did use it on the drug dealer, but that is because the crime was immediately affecting him, in his line of work, and was in his way.
It is entirely possible even the money changers didn't accept Republic credits; 'The Republic doesn’t exist out here' seems rather final, and against the idea of them accepting Credits for local money. He was an outsider trying, for the most part, to be under the radar and so minimized his use of Jedi powers; there wasn't anyone friendly to the Republic there to back him up, and being caught mind-tricking a cashier to accept a credits trade could bring unwanted attention down on him.
In the event they might have accepted Republic credits, given their vow of poverty, I would postulate they were more as the way nuns and priests operate, given cards to be used in the line of duty, but not removed them from the system to be exchanged for currency, where they could not be tracked for usage.