Well, the short of it is that I do not think Connections would be a good fit for you as it doesn’t seem to have some features that would be a must. I outline the areas Connections will not meet your needs…
A custom template could be done for you. I have a dev I could recommend that has plenty of experience working with Connections and its templates.
Currently Connections does not support custom fields. This is implement in the dev version and will be part of the next release. However, it would still require a dev to add the fields as there is no point and click method to add them yet. It is just the under laying ground work support that is complete.
Connections does not have a form builder and it does not integrate with other form builders. I does have an extension, called Form, but this is more or less a “static” plug and play form. Sections can be turned off, but that is about it is as far as customization.
An entry can have multiple n-addresses. Not sure that would completely meet you needs because you could not really define or notate which address is which parent’s home.
There also would not be a way to enable a parent to have editing access to each of the children’s entries. They would only be able to edit their own entry (if the Link extension is installed) if one exists.
There is no integration with mailchimp or other bulk email service.
There is not a method for entries to communicate with other entries within the directory.
At some point in the future Connections may be a fit because much of this could be done with features I have planned as well as extension I want to develop for Connections. But this will not happen in any time frame to be of use to you now, sorry.
It almost seems like you need a custom BuddyPress setup. Have you thought about tackling the problem from that angle?