Tinker, I don't call myself Demented for nothing, I'll walk into the lions den and give it a go.
I am a SAHM, I am very fortunate to have the circumstances, some of them created, don't live in an expensive house, share a car with DH, like shopping for bargains etc as it is very important to both DH and I that I am at home for DS (and soon to be DS2). I also know that some mums have to work even although they do all of the above and I admire them for the juggling act they must have to perform every day.
I personally prefer being referred to as a full-time mum rather than a housewife, after all being a mum is the most important job that women have and I would rather have this acknowledged than the fact that I also wash everyone's dirty knickers and make the dinner etc.
I also feel that if I did work outside the home that I would not feel that I was a part-time ... and a part-time mum. Surely you are always a mum, at any time the phone could ring to say your child was ill etc and you would drop everything and go. However when at home with your child I would not imagine there would be many mums who would be worrying about how the office is coping without them and certainly if the phone rang saying they were in a state could the mum come in I don't think many would abandon everything and go the same way as you would for your child. After all this would be your day off from work, you can never have a day off from your child, even if they are in someone else's care.
If I ever have a babysitter (a rarity) I don't feel that for those couple of hours I am not a mum. I still worry about DS, think about him, perhaps phone the carer to check he is OK, buy him something if I am at the shops and if I was needed I would be straight round to him. I feel it is like when you have newborn baby and the realisation hits you that even when you go to bed you are still working, you cannot finish at 5pm and forget about it, even when your child is sleeping you are on call.
Just because you are not there for that few hours, can't surely mean that you are not a mum for those few hours. If I am still at home when my children go to school and they are away from me, does that then make me a part-time mum and a part-time housewife or layabout (chance would be a fine thing)?