Don't worry about your daughter sticking out. Many, many different people vacation in Budapest now, so sticking out is not an issue. Much has changed in the city since Communism fell.
In Budapest, you will see so many different outfits and types of people that she will not feel out of place. If you go to the small villages, where many of the people are still living in the past, then your daughter will be stared at, and she may feel uncomfortable. Of course, she will be stared at in Budapest, too. This is just what happens in Hungary. We look at people and we don't feel embarrassed when caught looking at people. In the small towns, where most of the people are used to seeing the same inhabitants every day, any newcomer is looked at, no matter how they are dressed. In Budapest though, it isn't as intense. And, it isn't done with any malice, it's just curiosity without the American sensibilities you are used to. This is truly just the norm in Hungary.
In the villages, most of the people are conservative. In Budapest, most of the people are liberal.
If you go to the pools or baths, be aware that, for the most part, Hungarians are very comfortable in their own skin, no matter the size of the person. We have a saying - "If you don't like it, don't look at it". So if the very large woman in only a teeny bikini, maybe without a top, is bothersome, or the old flabby man in a Speedo is too much for you, we just don't care! Hungarians love the water, and we like to expose as much of our body to the water as possible! It is healing, after all.
Now out on the street, the older generation will dress conservatively, but the younger generation dresses to accentuate their form. You will see some very skimpy outfits on women under 30. Eh, sometimes over 30, too! The "Me Too" movement is just starting in Hungary, and I did notice some of the whistling from males directed towards attractive females is not as noticeable, but the whole mindset of Hungarians is focused on showing off their beauty, and it will be a long time before men in Hungary act like men in America in regards to women. So if you do hear a whistle towards your daughter, please don't be offended, the intent is not to make a woman feel objectified, but rather to express admiration. Different culture, for sure.
If I may offer a suggestion of a place to go, since it has been so long for your husband and his father, if they may like to feel some good old Hungarian pride, go to Ópusztaszer. It is south of Budapest by a couple of hours, and it is a beautiful open air museum where you can see how the Hungarians lived when they first crossed the Carpathians and settled in the valley. There is a rotunda with a painting done in a circle, and there is quite a bit of history as to how the painting came to be. I wish I could've taken my son-in-law there when we went this summer, but alas, we were not in Hungary as long as I would've wished, and there were a lot of relatives to visit. But if you are there for 2 weeks, maybe you will have time for a day trip!
Also, Lake Balaton.
Truly there is so much to see and do, and your list may be long after going through the guidebooks! If you need any help figuring out what sights will be truly worth it and what can be "if we have time", let me know and I don't mind giving you some feedback. I realize I am a bit biased towards all that is Hungarian, but I can also be objective if I have to be.