I think your alterations/sewing lessons combination can be a good business. I would ditch the birthday parties. It would be too difficult to market the business if it is all over the board. Stick with the sewing end of it. Work it from home if at all practicle to contain the expenses. I would advertise in my local park district brochures since they generally are distributed to all homes. Families are drawn to those types of ads. You can target women as well as young girls (not to say males couldn't be your customer too, but traditionally it's more female).

I recently was trying to teach my adult daughter to use a sewing machine and I wished there were some classes she could take. I can see a market for this. Good luck!