Just a follow up, I found a document titled Interspecific Hybridization of Prunus by Richard E.C. Layne and Wayne B. Sherman published in HortScience, Vol. 21(1), February 1986. If I am understanding the document correctly, it seems to indicate that P. spinosa x P. cerasifera ; P. spinosa x P. salicina ; P. cerasifera x P. domestica; and P. domestica x P. spinosa have all been created. The document does indicate that from a fruit cultivation perspective the hybrids tend to be less productive, may have pollination issues, and likely multiple backcrossing cycles would be needed to provide a good fruit. Given this, it seems possible to cross P. avium with P. domestica but there is a real possibility that the resulting plant could produce a poor fruit or have fertility problems. In the event that the plant were to be fertile, it seems it could then be crossed with P. cerasus, so the original post could be possible.
Another thought is that P. cerasifera X P. salicina is known to be a good combination. It also seems that commercially viable P. avium X P. salicina has been achieved so potentially P. avium could be crossed with P. domestica by using P. cerasifera and P. salicina as bridges for pairing capability.