Note that the phrasing of GWF - and most features/feats of that sort - states that you "can" do it, not that you "must". Whenever a feature/feat (including Great Weapon Fighting) is worded this way, it means that the player can choose to do the specified action/behavior, but they can also choose not to do so.
Regarding the usage of Suggestion to cause a creature to attack its ally, the description of Suggestion states:
You suggest a course of activity (limited to a sentence or two) and magically influence a creature you can see within range that can hear and understand you. Creatures that can't be Charmed are immune to this effect. The suggestion must be worded in such a manner as to make the course of action sound reasonable. Asking the creature to stab itself, throw itself onto a spear, immolate itself, or do some other obviously harmful act ends the spell.
The target must make a Wisdom saving throw. On a failed save, it pursues the course of action you described to the best of its ability. The suggested course of action can continue for the entire Duration. If the suggested activity can be completed in a shorter time, the spell ends when the subject finishes what it was asked to do.
You can also specify Conditions that will trigger a Special activity during the Duration. For example, you might suggest that a Knight give her Warhorse to the first beggar she meets. If the condition isn't met before the spell expires, the activity isn't performed.
If you or any of your companions damage the target, the spell ends.
Sage Advice does address this kind of usage of Suggestion here. In response to a question asking whether Suggestion can cause a target to attack another creature, Mike Mearls suggests:
Only in specific situations - would have to play upon existing rivalry or anger. Ex - Guy you suspect is a traitor really is.
Chris Perkins says:
It can, but if the spell's target thinks the suggested action is likely to cause it harm, the spell could fail.
One could certainly argue that you attacking an ally is likely to result in you being harmed. The caster would need to word the Suggestion carefully if they actually want it to sound reasonable.
If the caster does manage to word the Suggestion convincingly enough in just the sentence or two specified, and the target fails its Wisdom save, then it does indeed pursue the course of action to the best of its ability - which would presumably mean it would not hold back when making such an attack.