I have a slightly different take.
All 4 kids should apply to schools that are a good fit and see what the aid packages are like.
I don’t think there is an issue if the family pays different amounts for each kid. They are providing them with the equal opportunity to attend college.
The only way I’d have an issue is if one of kids was told explicitly that they couldn’t attend school X because family resources were being used to fund another kids choice.
If there is a gap between expenses and available resources, then it seems like a perfect example of how a Plus loan is a good thing.
In terms of using the house proceeds–based on the facts we have I do think it OK to use them for the tuition of all of the kids.