I agree with what Eva Elizabeth said!
It’s totally possible. Not all have problems with being alone, and as Eva Elizabeth said, I have no doubt that a good positive trainer would have no problem preventing that. I was very careful making sure that all of mine were used to staying alone (and in different combinations because that happens here too!) but it just took some thought. Like socialization. They are not difficult dogs. While, like all breeds, there is a lot of variation from individual to individual, I think more would make good therapy dogs than not. I picked all of mine thinking more about sports potential, and even totally NOT looking for therapy dogs, 2 of the three could do that job with no problem at all. The oldest one is not trained as a therapy dog but has certainly filled that role with both elderly relatives and small children for years. He is incredibly empathetic to people who are in distress and will gently just go lay his chin on their laps. They often don’t even realize they are patting him as they talk until they look down and notice what they are doing!
One thing I would caution against, however, is “thinking” about a “bigger” Havanese if it is really important for you that the dog travel with you by plane. Guessing the grown-up size of any particular puppy is just as difficult as predicting the size of a human baby. you can certainly ask the breeder to make an educated guess, but from there... they do their own thing! And the size of the puppy when it leaves home is not always completely predictive. My older guy was the largest puppy in his litter, but his parents were not “large” Havanese... they were middle of the road, “average” sized Havanese, about 12 lbs if I remember right. My breeder did warn me he’d be on “the larger side”, and I decided on him for completely different reasons, and have never questioned my decision. But an “airplane dog” he is not.
Conversely, my “middle child” happened to be born within a day of a litter bred by a nearby friend of mine, so the puppies sort of grew up together. Pixel was always a little bigger than her puppies as they were growing up, and my friend kept predicting she would be larger. As adults, Pixel is actually smaller than all the puppies in that litter ended up except for one. She grew earlier, they grew for longer.
“TECHNICALLY” My big boy fits the airline size regulations... he is 11 1/2” tall and 17 lbs, and he is within standard for our breed. But it would be like putting a hotdog in a bun. Yes, he could stand and turn around, JUST BARELY, by playing pretzel (we’ve tried the largest airline approved dog carrier on for size) but it doesn’t look the least bit comfortable for him. It is certainly not something I’d ask him to do with any regularity.
My girls are 10 1/4” and almost 13 lbs, and 10 1/2” and 10 lbs. Yes, you read that right... the taller one is lighter boned, both are in excellent, fit, sports weight. EITHER of them would fit in an airline carry on without a problem. So what I REALLY think you want is a Havanese that is in what our breed standard calls our “ideal” size range of 9 - 10 1/2”. In that size range, you shouldn’t have a problem with airline carry on. If it is a deal-breaker for you if the dog CAN’T fly with you, look for breeders who tend to produce dogs toward the lower end of that size range. (And there are many these days)