StoryProgression is a very far reaching mod that takes over the control of all inactive sims in town, replaces the often broken EA version of story progression, and yes it also handles genetics and immigration.
http://nraas.wikispaces.com/StoryProgression+FAQ
(scroll past the 17 internal links to get to the readable part)
Although very popular, if this was all you wanted then Overwatch also has an option to Clean Up the Homeless on its overnight runs.
I prefer to have both mods not do this and just keep an eye on the size of my homeless population with MasterController. If it doesn't get out of hand, for me there isn't much of a problem. Sims shouldn't be getting stuck just because they are homeless, they should be going off the map or into the darkened out units of LN type apartment buildings if you have any of those to hibernate when they aren't needed.
I guess the question really is, do you want these adopted kids to be alien hybrids? If not, the alien percentages can be set back to 0 using MC Cheats.