The details are not yet out about the stimulus, but it is believed that payments will be determined based on information on the 2019 tax return if it has been filed, and the 2018 tax return if it has not.  

If your children were his legal dependents for tax purposes in 2019, it would follow that any portion of payment intended to go for the children would, unfortunately, go to him.  

At this point, however, we still do not know details as the stimulus bill is not yet law.

We will be posting updates HERE as soon as we have good, accurate information that you can use.  

I am sorry that I don't have better news for you today and perhaps something is in the bill that will address your situation, but at this time we just do not know. 

I've come across more information on how these stimulus rebates will work.  The link  below is the best analysis I have come across and should help a number of those on this thread understand 'who claimed who' and how this appears it will settle out:

https://www.cbh.com/guide/alerts/cares-act-what-you-need-to-know/

(scroll down to "Recovery Rebates")

Basically, the stimulus payments are an advance against 2020 tax returns. 

When we complete 2020 tax returns, we will each re-calculate the stimulus payments based on 2020 tax returns  (income, qualifying children, etc).  

Whatever that re-calculated number is LESS what you already received will be an additional credit on your tax return, which would increase your refund or reduce how much you owe.  Let's say you didn't claim a child in 2019 but did in 2020 as an example that could create the credit

And here is the kicker, if that recalculated number is negative (meaning your stimulus payment was higher than you were really entitled to based on your 2020 tax return), YOU WILL NOT owe that money back.  Let's say you claimed a child in 2019 who was 16 but in 2020 they were 17 as an example on how the recalculated number could be negative,  (a 16 year old is a qualifying child for the $500 but the 17 year old is not eligible)