Should I file jointly with my common law wife or separately with each of us claiming one dependent since our youngest did now receive early child tax credits?

Below is a link to help you decide if you are considered as married.

There are many factors that go into deciding how to file, but most are spelled out by the IRS. 

A child is either your dependent or not by IRS standards. 

If you are considered as married, it won't matter much how you file, Married Filing Jointly or Married Filing Separately since most all your combined income and credits would be split between the two of you. (That is what Common-Law does). 

Additionally, there may be credits you are no longer eligible for when filing Married Filing Separately. 

With that said, the Advance Child Tax Credit payments are not link to any particular child. 

They have always been an advance payment for the credit you will get on the 2021 Tax Year Return. 

On your Tax Year 2021 Federal Return, the credit is calculated, the payments you received are subtracted and the difference is what is added to your refund (or subtracted from the tax balance you owe).  

In your situation, you received half the payments based on 2 dependents.

When you file, you can claim your 2 dependents and get the remainder of the Child Tax Credit. 

If the new-born's mother files and claims the new-born, you would have 1 dependent on your return and be claiming Advance Payments made based on 2 dependents. This would result in little or no remaining credit on your return and she getting a full credit (no advanced payments received) HOWEVER there would be an issue of whether she or you would have the right to claim each child. Only one of you could have supplied more than half the support in the household. The IRS has rules as to who can claim dependents in a household, you can't just split them up however you want.

If you are both members of the same household, decide which one of you has the right to claim the children. 

Next decide if you are considered as married in the state of Texas, and, if you are, whether to file Married Filing Joint or Married Filing Separate. (as I said, income and credits are allocated either way).

Claim the 2 children as dependents on your joint return OR the return of whomever has the right to claim the children as dependents .

The issue which may impact your tax liability the most this year is not being able to claim Head of Household. 

Link about common law in Texas

IRS Rules about claiming dependents

Since you are not technically married, the only way you can file a joint tax return is if you are living together in a legal common law marriage. For those states that will recognize a common law marriage certain steps had to be taken. contact an attorney if you are in a state that recognizes CLMs. Those states require certain affirmative steps before a CLM is recognized such as registering the CLM. see below for those states..

if your state doesn't recognize CLMS. that at best each of you could claim a dependent (not the same one) and file as head of household 

• the states or districts that recognize common law marriage: Alabama, Colorado, District of Columbia, Kansas, Idaho (if created before 1/96), Iowa, Kansas, Montana, New Hampshire (for inheritance purposes only), Ohio (if created before 10/91), Oklahoma, Pennsylvania, Rhode Island, South Carolina, Texas, Utah;

Head of household

1) Did you have any dependents? – if no you can not file as HOH
2) If yes, was the dependent claimable solely because of a multiple support agreement – if yes you can not file as HOH
3) If no, was the dependent legally related to the taxpayer - if no you can not file as HOH
4) Were you a nonresident alien at any time during the year -  if yes you can not file as HOH
5) If you were not legally wed on the last day of the year, see A, if you were see 6
6) Were you legally wed to a non-resident alien at any time in 2021, if yes see A, if not see 7
7) If legally married were you legally separated at the end of 2021 under a decree of separate maintenance, if yes see A if not see 8
😎 Did you maintain separate living quarters from your spouse, if legally wed, for the last 6 months of 2021, if yes see A, if no you can not file as HOH

A. was the dependent a married child of the taxpayer? if yes, will the dependent child file a joint return with their spouse? if yes you can not file as HOH. If the dependent child was not married or if married will not file a joint return with their spouse then did the legally related dependent use the taxpayer’s household, for which the taxpayer paid at least ½ the cost, as their principal place of abode for more than ½ the year – then you can file AS HOH