July 10th 2024 I was awarded temporary custody of our children. She filed first but apparently made up a W2 to beat me what form do I fill out to obtain 2024 full tax?

If she had physical custody of the children for more than half of the year (the most nights) she is entitled to claim them for 2024. 

You should be able to claim head of household and all four of your children as your dependents on your tax return, regardless what the tax prep firm says, assuming you have physical custody of your children for more than 6 months in 2024.  Worst case scenario is you may have to paper-file your tax return instead of e-filing if she had filed her tax return and claimed the children before you.  In that case, the IRS will reject your e-filed tax return.  Just print the tax return on paper and snail mail the tax return to the IRS. 

The law is on your side, the custodial parent is presumed to have provided more than half of the children's support unless you have signed a Form 8332 to allow her to claim the children.  This is regardless of what the divorce decree says. 

Use a different tax prep firm, if necessary, or use TurboTax if that tax prep firm refuses to prepare your tax return.  Good luck!

Here is what Copilot says about head of household and Form 8332::

The term "Head of Household" (HOH) refers to a tax filing status that you can use if you are unmarried and maintain a home for a qualifying person, such as a child or relative. To qualify, you must pay for more than 50% of household expenses and live with a dependent whom you support for more than half the year. Filing as Head of Household offers benefits like a higher standard deduction and lower tax rates compared to filing as Single. 

IRS Form 8332, titled "Release/Revocation of Release to Claim to Exemption for Child by Custodial Parent," allows custodial parents to release their claim to a child as a dependent to the noncustodial parent. This form can be used for current or future tax years and is essential for ensuring that the noncustodial parent can claim the child tax credit and other related benefits. Additionally, custodial parents can use Form 8332 to revoke a previous release of this claim. For detailed instructions on how to file, you can refer to the official IRS page.