You're right: the 4th Battalion. According to the House of Tartan's Tartan Finder, it was used for the pipers' plaids. (The drummers' also, I would presume.) The regular soldiers of the regiment wore Leslie tartan trews.

I believe you're right about it being Sir Douglas Haig who adopted the tartan for the Haig family. The Buccleuch Check tartan descriptions mention Earl Haig, and there have only been two Earls Haig so far, the first much more well-known than the second. Sir Douglas Haig was an honorary colonel of the regiment (or the battalion, if the tartan descriptions are correct).