Parent/Child sum when each parent has different number of children (and the excel is formatted poorly)

Question

I've looked all week for a solution to this - would love some help.

I inherited a (maybe poorly designed) excel.

I would like the cells in the blue highlighted line to sum the values for the month only for the children associated with the bolded parent name.

in the image attached to this post, I'd like cell D4 to add all Jan totals for the Column B "parent 1"s but not any other Column B parents.

I would like this to be a formula I can use on this sheet, as opposed to pulling from a pivot table, in case i change the monthly value for a child here and there.

parent and child relationship excel

I was having a hard time phrasing this in copilot and on google, so I got nowhere asking for this. Sumif and vlookup didn't work, and this isn't something I want to use a pivot table for because I need automatic updates if a value in a cell changes.