LOL you are as usual comparing Mohammad with yourself and your daddy, a prophet does not do things at random, a prophet only does whatever is willed by Allah. when allah says take your women and nafs with you, prophet wouldn’t think like ‘ok, I’ll take with me whoever’s house comes first on my way to mubahilla’ NO
someone more important had to be chosen to glorify Islam and trimpuh over christianity, and they were only ahle bayt. (please note that he could take one of his wives with him as well)
You say his other daughters were married, so was Fatima.
Mubahilla was not a usual get-together, some serious cursing was going to take place and someone was going to be doomed, don’t trivialize the importance of that event.