What is the easiest way to concentrate a solution without causing it to hydrolyze?
Try adding Na2SO4 to the mix and freeze forming Na2SO4.7H2O. Slow, but at least, no oxygen-related chemistry, discussed below.

As a sidebar, you likely have formed basic ferric acetate from boiling, which adds oxygen, to your acidic (vinegar) and aqueous ferrous acetate mix. 

Likely reaction mechanics are complex, see, for example, Table S1 here . Per the source my take of a possible reaction sequence:

$\ce{ O2 (aq) + Fe^{2+} → Fe^{3+} + .O2− }$ ( moderately fast) )

$\ce{ . O2− + Fe^{2+} + 2 H+ → Fe^{3+} + H2O2}$  (fast )

$\ce{ H2O2 + Fe^{2+} → Fe^{3+}  + .OH + OH− }$ ( slow)

$\ce{  .OH + Fe^{2+} → Fe^{3+} + + OH− }$ ( fast )

Net radical reaction: 

$\ce{ O2 + 4 Fe^{2+} + 2 H+ → 4 Fe^{3+} + 2 OH-}$ 

The creation of FeOOH is also possible in less acidic conditions per his source: 'Air Oxidation of Ferrous Iron in Water'.