First of all, thank you for introducing your daughter to traditional Scottish music! The best places for live music sessions are Sandy Bell's, the Royal Oak, and the Diggers Arms, although there are other venues around Edinburgh.
You didn't say when in February you'll be in Edinburgh, but the Edinburgh Folk Club has two excellent concerts lined up for mid February. They meet every Wednesday in the Pleasance Cabaret. On the 13th. they are presenting Tony McManus, who is a superb Irish fiddler. On the 20th., the Tannahill Weavers will be performing. They are one of the best traditional groups in Scotland, so all of you would be in for a treat. They have been together for 50 years in various incarnations, and this is possibly a farewell tour.
If you decide to see the Tannies, I'd advise making reservations. That one is bound to be sold out soon.
Sandy Bell's has sessions most nights, and Sunday afternoons.
Enjoy the music!
p.s.: You shouldn't have any trouble at all bringing your daughter in to the pubs for live music, as long as she doesn't order a beer!
p.p.s.: I just checked the EFC website. Tickets are still available for the Tannahill Weavers, and they are very reasonably priced. Your daughter may be able to obtain a student or concessions ticket, which is even cheaper.