If the fleet leader is the ship you want, selecting the fleet by the fleet icon should give you that ship.. I've not seen it not work, but I haven't paid attention to replacing lost ships. I don't know of anything you could do if that's not doing anything as you say.

I don't think there is a way to control where it is in the stack. 

You can scroll through ships in a fleet or stack with the TAB  / SHIFT TAB key, and since caps are at the top, this gets to them quickly.  I normally hotkey critical capital ships so I can pull them up immediately.  You can also create fleets with the Progen as the flagship by Tabbing to the Progen before you create the fleet.  When you select the visual tab for that fleet, I'm pretty sure the Progen will come up first, though I am not positive since I don't normally manage my ships this way.  Finally, you can select the capital you want with a click in the Empire tree.

I know this isn't specifically what you asked, just explaining how I do it.  When you get a ton of ships, it can be a challenge to get to the one you need.

It was a perfectly valid question, Sith, one I was wondering about also.

Not intending to hijack the thread, but I have another related question.

I use the stack view for the empire tree so that it's not unbelievably cluttered.  However, I've noticed this causes problems with tabbing through units.  It will only tab through the various stacks of ten it arbitrarily creates, rather than each individual unit, which is a problem when I need to micro individual abilities.

For instance, say I have 5 Iconus Guardians whose abilities I need to pop in sucession.  I pop the first one, then press tab.  My selection changes to a new unit in that group.  Good.  I wait 'till the first one runs out then pop the second and press tab.  Problem.  My selection is now stuck on the second Iconus Guardian.  Deselecting and then selecting the stack again yields differing results, but the tab selection always gets stuck on the second unit when less than 10 are selected.

Say I have 12 Guardians instead (for the sake of argument.)  If I tab through these, it switches back and forth between the same two units over and over - the arbitrary 'top' of each stack.  In the empire view, the selection changes between one little stack of ten and the stack of two.

If I switch to normal view for the empire window, tabbing works as expected.  But with a heavily populated or fortified grav well this view just is not feasible for me to work with!  Does this happen only to me?  What can I do?

Easy solution - get a bigger monitor that runs a higher res. This means more room on the side due to more height. Hence you don't need to stack the empire tree and can view the whole thing

(Caveat - I didn't say it was a cheap solution, just an easy one!!!)

When I play the empire tree does fill up. The solution I use is this. At the top left of the screen is a push pin icon. This icon pins the said planet, ship, or structure to the empire tree. The default setting is each planet is pinned along with capitol ships and starbases. I keep this clean!! I de pin every planet except for the one or two main planets that are at the front lines and get a lot of combat and late game i remove them completely.

(Do not forget to set your frigate factories as a group. I make frigate factories grouped as control+0. This way im not struggling to try and zoom out to click on the planet that has the factory in it. I just hit 0 and then build what i need.)

Next, ships in phase space have their own spot on the empire tree. When they jump they appear directly under  your fleet icon and disappear again when they exit phase space. This tends to make the empire tree skip around which is a major pain in the ass when you are trying to micro a battle. Since you cannot de-pin this carrot MAKE SURE TO MINIMIZE IT, it will keep it that way until you start the game again after a save or start a new one.

If you have more that one fleet with capitol ships in it....you can click the carrot of the planet they are at to close the planets tree so that you will again be able to see the main fleet by itself. This is especially needed when the Advent are in combat with you and they have 5 or more guardians and they activate the "you cant see crap ability" which for some reason the developers have yet to find some better graphical representation for the shield share.

Hope this helps.

I believe that when the stack units option is on, the ship with the most damage is moved to the top of the unit stack (so you can see how bad your unit is damaged). Thats not a solution to your problem, but I wasn't sure if you knew what was going on and why they might seem to jump around a bit (actually, im not sure when the switching occurs, i've just noticed that the one showing has the most damage).

As for solutions, well, everyone was telling me to basically create more fleets. so, make 1 fleet that just has your capitals, 1 fleet that has just your guardians, 1 fleet thats all your illuminators, etc. turn unit stacking off. You still probably want to move all your ships at once to 1 location, so make sure you select all those fleets at once and save it to a number (dont forget to set combined move). When adding replacements, it might get a little micro crazy because the ships might not join the intended fleet (probably the capital fleet), but you could easily select your guardian fleet and micro them that way.

btw, for anyone who just drops into this post and might get confused:

the original post was about where a unit appears on the empire tree. if you maximize a fleet icon that appears on your empire tree, then click the icon (to select all the ships), 1 ship's abilities appear on the UI at the bottom. There are various ways to pick a different ship so as to use different abilities, but the question was about changing the default.

the new question is about unit stacking, which can be turned on/off, and cycling (using the tab key).