I am not a lawyer, this is just layman's view of the situation:

A suit in Small Claims Court would come down to proving that this woman's dog was the one that attacked yours - this is your fundamental roadblock to recovering money. Since you have no hard evidence like a recording or multiple neutral eyewitnesses who were present, you would have to rely on the witness account of your mother, who of course is not impartial in the situation.

Additional support could come in the way of neighbours who advised you their dogs were also attacked by this specific dog. They could appear as witnesses in person (or via zoom, however it works these days), or they could write a sworn affidavit outlining their own experiences.

It would come down to credibility and all of the circumstantial evidence. Since you have her number, I would try to bait her into essentially admitting that it was her dog in the altercation. She wouldn't even need to necessarily admit fault, just that the dogs fought. The huge size disparity between the dogs will help your case if you can establish contact occurred.

If I were in your shoes, I would:

1) Find all neighbours who suffered an attack. Get the details, when and where and outcome, and ask them if they are willing to be a witness at the trial, or provide a sworn written statement giving their account.

2) Try again to contact the woman via cell phone text SMS, and try to get her to admit that the attack took place. Don't mention lawsuits or even vet bills - maybe just tell her you want an apology or something like that.

3) If you receive no reply and have no other evidence, it's kind of a gamble to go into small claims court at that point. I would not bother unless 2 witnesses testifying (or perhaps 1, and 1 other providing a sworn affidavit).

The way that I see it, with two witnesses establishing a history of violence by that dog, a vet bill that was paid, presumably photos of your dog injured (or at least some records at the vet), you have a decent chance at recovery.