I spent 3 months wandering around in Morocco a few years ago, alone. It is a fabulous place and I do recommend you take the opportunity to go, if you can. I'd agree that Tangier might be best skipped - I spent about 10 days there initially, and then a few more on my way out, and it was...trying. And not the most interesting place. Still, it's harmless enough if you're passing through and there are some great walks around the edge of the medina (by the sea) and up to the kasbah. Be prepared to get lost but don't panic.

My favourite places were all towards the south, and/or inland, where you get away from the crowds and the hassle. Places I would suggest for mother&daughter:
Essouira is an amazing walled town on the sea (but busy);
Meknes had a pleasant and non-threatening atmosphere and a Europeanish new town, with the rambling ancient medina as well and some monuments, and it's handy for Volubilis (the roman town, ruined of course).
Rabat is fairly cosmopolitan, with a touch of the ancient and a good souk (market); I loved Casablanca as well but many don't.
The Todra Gorge is heaven on earth (two hotels, no village, no electric after midnight: perfect peace under a zillion stars if you sleep on the roof) - but probably too far away if you're only there for five days.
Marrakech drove me mad.

If you're concerned about safety, it's not nearly as bad as some would have you believe. You get hassled in the market, yes. If you want a guide, fine; if not, a firm no and a smile usually does it. What doesn't work is arrogance, ignorance or silence: the surest way to get an unshakable pest is to be rude to them. Obviously you want to avoid walking in dark and dubious places after dark etc. Use your head, be modest, be civil and keep an open mind and you'll love it. Make yourselves some women friends - they're genuinely warm and welcoming and family life is great.

My 55-year-old (not well-travelled) mother went earlier this year and LOVED it. Sounds, smells, faces, nifty things to buy and eat. Go for it. Check temperatures though - won't be too warm.