Is there HMM that looks two elements back?

I think the keyword you are looking for is Higher Order Hidden Markov Models. Your "ordinary" HMM would be considered a First Order HMM. So yes, there is literature these types of HMMs.

An extension of Bayesian Network, Dynamic Bayesian Network (DBN) and 2-TBN in particular (looking at 2 time points at a time), or X-TBN (if you wish) can be useful here.

A node in such DBN would be a probability variable that represents the current state of an HMM represented by that node. Specific structure of DBN is up to you, you can for example incorporate different levels of HHMM (hierarchical HMM) into that DBN which also contains nodes that represent t-1 points in time.