How to get a colonial nation to trigger

Manpower is a crucial factor in creating and maintaining larger armies.

From the ingame help text:

Manpower represents how many able men of military age your nation has available.

Manpower is used to recruit new troops and to reinforce armies that have suffered casualties in war.

Whenever you want to recruit a new troop, you have to "pay" 1,000 manpower. If you don't have enough manpower, you cannot raise new troops.

When your troops lose men in fights or because of attrition, they will automatically be restocked from your manpower pool. If you don't have enough manpower available, replenishing your troops will happen a lot slower. (capped by the speed with which your manpower regenerates)

The exception to this are mercenaries, which do not drain manpower when being built or replenished. Low manpower is one of the main reasons why you would want to recruit mercenaries.

To sum it up: Manpower can be a deciding factor in war. You will find that if you are taking heavy losses during war you will not be able to replenish your troops fast enough or raise new troops because of low manpower. This might give your opponent the necessary edge to conquer your lands.

You can find more info about the topic in the EU4 wiki entry on manpower.

The only thing I can think of to enable you to influence the war without actually declaring war and hence drawing in the British is to provide War subsidies to Castilian Mexico.

There's no guarantee that your money would be wisely spent but it could sway things if it's evenly balanced.

You could also try to enforce peace on British Mexico. It may work, but if they refuse you'll be dragged into the war on the side of the defender.

Or finally you could try to support rebels in British Mexico or If you've researched espionage ideas 6 you could try to sow discontent to try and cause a rebellion uprising.