@dustynrobots a little confusing but let me settle the HOH aspect.
HOH is NOT predicated upon who earns the most money; rather it is based on who provides more than 50% of the household expenses (admittedly, many times who makes the most is also the one that contributes more than 50% of the household income.)
So whomever provides more than 50% AND claims the 18 month old files HOH and the other files Single.
Alternatively, there is nothing that precludes the person providing less than 50% of the household expense from claiming the 18 month old and in that situation both parents would file SINGLE. (One parent would meet the requirement to claim a child, but not be able to meet the over 50% household expense requirement while the other parent would be able to meet the over 50% of household expense requirement but not have a child to claim).
Does that simplify things?
