The current trend for two piece rods is likely to make a difficult task even harder. There are so many variations in action and strength amongst rods labelled as "carp waggler", "commercial", "pellet waggler", or similar, that rods suitable for trotting can be found amongst them. You are very unlikely to find 10/11' rods aimed squarely at trotting, and marketed as trotting rods.
I have the 11' Drennan Matchpro Ultralite, which is bob on, but it's two piece. I've recently purchased a Garbolino Altima 10'. Also bob on, but not quite as light in action as the Matchpro and also two piece. It's not marked as a pellet waggler rod, just a "match" rod, but the marketing gumph pitches it squarely at commie fishing. It has a faster action than any commie rod I've previously encountered, which suits me just fine for beck/small river fishing.
If it has to be a three piece, I'd suggest you look toward some of the Pure Fishing brands (Abu, Shakespeare etc). They often have budget three piece float rods in their ranges. Prior to buying the Garbolino, I used a fairly cheap 10' Abu Enticer for years. Rubbish fixtures and fittings, but the action is reasonable, despite being a cheap blank. At 10', even cheap and relatively heavy blanks feel light enough in hand.