Glycine is cheaper than its methyl ester - it would be more economical to buy the amino acid.
But anyway - I don't have a great deal of experience with amino acids, but I have a little. I worked for a while with a poly-hydroxylated proline synthesis, and in order to isolate the zwitterion I used ion exchange.
If I were you, I would dissolve the amino ester in NaOH(aq), alcohol free.
Once the reaction is complete (I'd probably monitor by IR), acidify the mixture with HCl, to neutralise the NaOH and protonate the glycine (for this reason, I would not include ethanol as a solvent). Load your reaction mixture onto a short column of strongly acidic resin. The protonated amino acid will exchange with protons on the resin and be immobilised. The sodium cations will also be immobilised.
Pass deionised water through the resin, to wash out the HCl, until the effluent is neutral.
Now pass dilute aqueous ammonia through the resin (1-2 M is sufficient). The ammonia will exchange with your amino acid - it basically deprotonates the immobilised protonated glycine, freeing it from the resin. Collect the ammoniacal effluent, this is an aqueous solution of ammonia and glycine. Remove the water and ammonia on a rotary evaporator (in a fume hood otherwise you will stink the place out) to leave glycine.
Note: This will not separate glycine from any other amine impurities, so ensure the reaction is complete.