Ryan Adams provides guidance on using distributed transactions against Availability Groups:
A paramount concept to understand is how to make the DTC highly available. We can see from the precedence order that SQL Server will use the local DTC out of the box. This makes it appear that everything is working, and it is, but it is not exactly highly available.
I see a lot of customers leave it configured this way because they either don’t know the ramifications or do not realize they are using the MSDTC (Linked Servers). Since it simply works out of the box, things get left this way until they end up with a suspect database and error messages that look like this:
“SQL Server detected a DTC/KTM in-doubt transaction with UOW {598B7EDD-F7A1-9DC1-8D3E-303A4C93AAB4}.Please resolve it following the guideline for Troubleshooting DTC Transactions.”
Read the whole thing. There are a lot of small areas between processes where things can fail, and the combination of DTC + AGs is no different.