Scotland offers a range of child-friendly accommodation and activities suitable for families.
It's worth asking in tourist offices for local family-focused publications. The List magazine (available at newsagents and bookshops) has a section on children's activities and events in and around Glasgow and Edinburgh.
Children are generally well received around Scotland, and every area has some child-friendly attractions and B&Bs. Even dryish local museums usually make an effort with an activity sheet or child-focused information panels.
See also Lonely Planet's Travel with Children.
A lot of pubs are family friendly and some have great beer gardens where kids can run around and exhaust themselves while you have a quiet pint. However, be aware that many Scottish pubs, even those that serve bar meals, are forbidden by law to admit children under 14. In family friendly pubs (ie those in possession of a Children's Certificate), accompanied under-14s are admitted between 11am and 8pm. There's no clear indication on which is which: just ask the bartender.
Children under a certain age can often stay free with their parents in hotels, but be prepared for hotels and B&Bs (normally upmarket ones) that won't accept children; call ahead to get the low-down. More hotels and guesthouses these days provide child-friendly facilities, including cots. Many restaurants (especially the larger ones) have highchairs and decent children's menus available.
Breastfeeding in public is accepted and is actively encouraged by government campaigns.
The larger car-hire companies can provide safety seats for children, but they're worth booking well ahead.