I moved out of state then back, how would I put in my date of residency

What state? Every state has different forms and rules.

Your question might be unanswerable. I am certainly not familiar with the tax rules for all states, but whenever this question has come up in the past, I have never seen a tax form for any state that provided for two separate periods of residency. If, as is likely, that turns out be the situation for your state, I suggest that you contact your state income tax agency and ask them what you should do.

Note that the problem is the state tax form, not TurboTax. TurboTax can't handle a situation that the tax form does not provide for.

It depends on the details of the moves, including which states. In most cases, you should consider yourself a full year resident of the original and year end state and a non-resident of the state that you lived in in the middle.  That is, treat the middle state as only a temporary absence from your resident state.