As a British person, her use of the word tyke is absolutely plausible in this case. At least for me. The usage is basically her saying "he came out such a little rascal" and that's not unusual for a grandmother to say all the time when reminiscing (not the right word) about their grandchild. From a neutral standpoint, it makes more sense that she would call him a tyke than an anti-semitic slur.

However if you're certain of what you heard then it's just a case of he said she said and you need to gather more evidence. You may be a team but if he genuinely didn't hear it, he shouldn't be siding with you.

What are the other instances you're referring to?