We faced a very similar situation a few years back. We had 2 adult cats and a roughly 9 month old kitten. My honey was dying to have a dog. We both have asthma and allergies. We ended up with Chihuahuas. You can train the yippieness out of them, it takes work, but it can be done. They are smart little dogs and housebreak easily if you do your part in the whole crate training process. We got Deuce from a lady that only had a couple of Chihuahuas that she breed. Deuce was 9 weeks old when we got him. We had him fully housebroken in just about 4 weeks.
We kept in in a baby's playpen. It sounds odd, but it worked perfectly. We made half of the playpen the opps potty area and the other half the blankets, food, water, chewies, and toy area. He was so stinkin tiny, it worked out great. We kept it by the bed, if he woke up in the middle of the night, we would take him outside for a quick potty and then we would come back up to go back to bed. I say we, but it was usually my honey. lol
Chihuahuas come either with long or short hair. So, you still could have one with the long hair. I never thought that I would want a Chihuahua. They are so tiny, a little funny looking, and have a bad rep for being yippie. But, Deuce and Beanie are such little darlings. I wouldn't trade either of them for the world.
If you do decided to get a Chihuahua, I strongly suggest that you get the book Chihuahuas for Dummies. We found it to be a wonderful resource. As with most breeds, Chihuahuas have some quirks. They are heat seekers, so expect to have them always near/on you. They attach themselves to only one or two people, so expect that it's going to take some time to socialize them with other humans and stranger's animals. They sometimes have blood sugar issues and need access to food all the time during their first year or so.
I hope this helps. Happy puppy hunting! Maggie