In play I have a Drow Eldritch Knight with Dispel Magic. She attacks with her first attack and triggers Shield , Can she action surge, cast Dispel Magic on the shielded enemy and then make her second attack without the shield in place?
I am not sure what the rules say about this. I know you can split your attacks and do other things between them, including reactions, bonus actions and movement but I don't know about taking an entire action in the middle of another action.
Of course not every possible scenario is explicitly covered in the rules, one way or another.
There is only the rule about allowing you to move between attacks. There is no rule that once an action is begun, it must be completed before a bonus action is taking or another feature is used, including Action Surge.
Shield Master is a commonly used example. Unfortunately, JC has seemed to change his position on this, first saying the Attack action must be completed before the bonus action shove, and later saying you can Attack, bonus action shove, and attack again via Extra Attack.
In other ways, other examples are GWM or SS, and Reckless Attack. Accepting the -5 penalty is an option for each attack, it is not a "once you commit you are stuck with the -5 / +10 on all attacks". A barbarian with Extra Attack might attack normally, but then decide (after missing) to Reckless Attack on their second attack.
Consider this example: You make an attack against a target, reducing it to 0 hp. Your ally is fighting another foe, but they are 50 feet away and your speed of 30 feet is not sufficient. So, you choose to Action Surge, allowing you to take the Dash action, and close the distance to attack the second foe via your Extra Attack.
This is a case of Action Surge providing additional movement via the Dash action. Since we know you can move between attacks, this seems like it should be completely permissible.
Finally, looking at two other things: rule of cool (which this certainly would be!) and action cost: you are using one of your most powerful features (Action Surge) and expending a 3rd-level spell slot simply to allow you to make your second attack without Shield interfering. Depending on the AC in question with Shield added, you might have been better off using Action Surge to simply take the Attack action again, allowing you
THREE further attacks (albeit against the increased AC).
So, while
RAW I see nothing preventing this, and would certainly allow it, off-hand I would
highly suspect you would be better off using Action Surge simply to make additional attacks, without costing you a valuable 3rd-level spell slot. Perhaps the exception would be if your
dispel magic also helped allies attacking the same target?