Need some socialization advice

Hi! My puppy is quite reactive and pulls towards other dogs, especially smaller ones. (She is medium sized.) My puppy's trainer told me to let her meet as many dogs as possible outside, as her breed tends to become territorial and aggressive if they are not socialized enough. My puppy is 5 months now, and she likes dogs, but she is a bit rough with smaller dogs.

I let her meet some dogs on the sidewalk, and she usually does okay with bigger dogs. They sniff each other, and we move on. She gets excited, but we move along. I am hesitant about letting her meet small dogs as she lies down completely and jumps at them. She played on a loose leash with a big friendly dog that we already knew, with my trainer holding the leash, and she did well. (I want to add that she lies down for bigger dogs sometimes too, but does not jump at them).

So I don't let her meet every dog, and I try to keep her walking with treats. We are working on heel. I don't know if I'm doing right, and if dog daycare helps with socialization. I was thinking of taking her to doggy daycare for half day once a week to start out. It's a place that requires a 4-hour interview to make sure my puppy does okay with the other dogs. I don't think the dog park is a good place for her to play with other dogs as I don't know them, and I don't know anyone with a dog to play with mine.

I just feel unsure about all of this and don't know if anyone has advice for this.