Entering 1098T and obtaining AOTC--Do I have this right?

I have read and reread several threads.  Every time I think I have it all together, the details elude me.

 

Our child's university has been recording things incorrectly on the 1098-T, basing box 1 on charges not payments in a given year.  We didn't understand that was what happening last year (her first semester of college).  So we'll have to amend her taxes to be taxed on more of the scholarships/grants.  I think in answering this year's tax question, I'll know how to amend it.

 

So numbers (slightly simplified):

$10,000 Payments to schools for qualified expenses

+     120 Books purchased outside the school for classes

$10,120 Total qualified expenses paid

-    4000 AOTC

$   6120

-    7700 Scholarships and Grants

$  -1580 What the child will end up claiming as taxable scholarship income

 

There were distributions from the child's ESA, but they are less than the expenses of room & board, so they would not be recorded.

Room&Board        >          ESA disbursements (1099-Q)

$9739                     >            $6061.08

 

Do I have the process of how to look at all that correct?

If so, there is the question of how to enter that all into TT.  We use the desktop; child uses the online.

 

The parent taxes should be done first and then the child's taxes. For the 1098Ts on ours we just enter $4000 as being box 1 and $0 for box 5 of the main 1098 and then proceed.  Is there any harm in listing the second 1098 (for a single CC summer course) but not entering a box 1 and box 5 amounts or best not to include it?--it asks if there is another and habit is to answer the question asked. 

Then on the child's taxes they enter the full smaller 1098 and the remaining box1 amount from the main 1098 (full amount less the $4000 used on ours) and its box 5 amount.  TT will allow recording of book expenses after the 1098T questions (true on the online version too?). TT will automatically calculate the excess scholarship money and record as income with a special notation.  There is no need to enter the 1099Q since it is more than fully offset by room&board.

 

So did I get that right too?

 

Thank you!