If I prepare a phenoxide and react that with methyl iodide should the phenoxide group react faster than amine group or do I get a too many side reactions?
Hello, I would try to synthesize the dibenzyl-amino function first by using benzylbromide in water or alcohol not to benzylate the phenolic group, and in a next step methylating the phenolic group. After that you can set free the aminofunction by hydrogenation. That will work, perhaps. Wish you success!
If you want to avoid protecting then deprotecting your amine just to carry out one step, then harder methylating agents may give you better selectivity. Dimethylsulfate should work better than methyl iodide.
An intriguing alternative is to protonate your amine in situ to prevent it from being alkylated. Add 1 equivalent of chlorosulfonic acid to methanol, very slowly in an ice bath as it will be very exothermic. This should generate monomethyl sulfuric acid and hydrochloric acid, which will protonate your amine and provide an electrophilic source of methyl. Add your amine as a solution in methanol and heat to reflux. This is just an idea, I have no reference for it and I don't know if it has been tried before; I just thought it might be cool to try.