Hi, as you say, there are several ways to look at this.
Division is sharing into equal groups, so a first step might be to actually share out counters and notice that there are some left over, or remaining.
She might have seen division shown as jumps on a number line, so in your example she could start at 38 and jump back in 3s to as near to 0 as possible, then count those jumps. She could also start on 0 and jump forwards in 3s. With both methods she will see the left over numbers are less than 3 so are a remainder.
She could do it with the bus stop method too, noticing that it's not exact, there are 2 left over or remaining.
For the fractions, using counters or a similar object and making thirds (sharing into 3 groups) and then counting 2 groups is a good first step. Drawings can help too.
Then she could think of it as a division and then a multiplication. So 12 divided by 3 is 4. 4 multiplied by 2 is 8. So two thirds of 12 is 8.
Hope that helps. I'd say, as a parent, helping her to find a way that makes sense to her is really useful. Then at school the teacher can focus on the more formal methods.