I'll give my two cents on it and Judewright can correct me where I am wrong.
For the heir, I would look for another mate while you wait for your chosen mate to age up. If you find someone, you can grab that townie and not worry about having a mate for your heir. You can work toward your heir's LTW, reading skill books or working on what is needed, such as athletic skills, that are required for the LTW.
I know that you can do either with family members, take them with you or leave them, except the parents, they have to go with the new heir and their mate.
I think you are allowed to move them to a temporary home, I did that, while the home I had planned for them was being finished. I had a home that I had built for an earlier game but needed some tweaking, so I moved them for a day to a very small starter home and then moved them to their new home. I had gone ahead and moved them as I wanted to get the female pregnant and was having problems in the old house (don't like moving pregnant sims).
Since they had over $300,000 I had no problem in finding them a home, just wanted to do some changes to make it easier to take photos. Put the house on a bigger lot (went from 30 x 30 to 40 x 40) which also allowed me to move the house to a better position, no longer in the middle of the lot.
You don't have to take your home with you, you can do so or find a new one, and you can remodel it at any time, as long as you have the funds and don't have to use the cheat to get the money.
Hope that is helpful to you, these can be fun to do, even though I am having trouble with one family and now lots of trouble with traveling; which I think is connected to installing IP, no proof except a correlation (which isn't causation).
Judewright can add in what I missed, correct me in any if I am wrong and I think it is okay for me to add in my two cents.