that does suck, considering you don't want a dog. However, like you said, it is their house, so they can do what they want.
Although, I do want to recommend to make sure they know what type a dog they are looking for by their temperament and lifestyle. Jack russell's and poodles are extremely hyper dogs, so there is a high chance the jackapoo would be hyper as well. I dont know if that would be a problem at all, but I know some people are not prepared to handle a hyper dog.
We've had poodles before and they weren't too hyper. I hear they're both smart breeds though so I hope it'll at least be easy to train. I'm a very neat, clean person and the thought of puppy poo all over the house gives me the creeps. I don't think hyper would be a problem though...we have a big fenced-in yard and we're all very active (running, walking, etc.).
I know how you feel, my mom got one dog that I did want, so I was like.. cool. But it turned out to be this insane pomeranian that is just, ughh. Also, I should mention that ever since she got that dog my cat isn't allowed in the house anymore. My cat who has lived her for 6 years has been exiled because my mom's dog doesn't like when it is in the house. I had to take care of it all the time too. Ugh. Then later AFTER I made it apparent that I didn't want another dog unless it was a big outdoor dog, she gets another one. This time a chihuahua. I have to take care of that one too. It sucks. I can't move out for another 3 years :P
But one thing that might be good if you go with them to get it, is that it won't have territory problems. The first dog my mom got hated me for the longest time because it had been at the house a few hours before I got home from school, so therefore I was the intruder and the enemy. Its no longer like that, but good lord for the time being it was a pain.