ouch. id at least try to make good with the mother. give it time - its cool that her mom cares about her safety. establish yourself as a mature, stable, independent and well-off young man. earn her trust.
in the mean time, a certain kind of double date could help. for starters, only take one of your closest, most trusted friends. this way, you know he wont get in between you and your girl, interrupting your game. secondly, something like ice skating would be cool.
its a ton of fun, and most rinks are big enough, to allow your friend to take his date AWAY from you and yours. have him go on the other side, that way youre isolated; so itll feel as if you two are alone. even though technically her friend IS there, to make her mom happy. and since your friend will be doing his job of keeping the friend away, you two wont feel awkward.
imo double dates usually arent a good idea in the initial phases, but in your situation it could be a lifesaver.