The real challenge may arise from the dissimilar materials and thicknesses more so than the power capacity.  But, an uneven heat balance can be compensated for with proper electrode selection.

If you are new to resistance welding then you might want to contact the RWMA (Resistance Welding Manufacturer's Association) and get a copy of the Resistance Welding Manual.  It will be money well spent.

If you are welding for aerospace then you might also want to pick up a copy of the AMS Resistance Welding Specification if you have not done so already.  It should have tables with weld schedules and qualification requirements (but maybe not for your material combinations).

Since you are welding dissimilar materials, some feasibility tests would be a prudent move.  Some of the machine builders might be willing to perform some demonstration welds if you can supply some blank coupons.

Without knowing more about your specific application it is tough to call out a power requirement.  The transformer size is also determined by the machine design, types of cables, and how the cables are routed.  The math is simple since it is all Ohm's law.  The trick is that you need to know the total resistance of the welding circuit.  If you are shopping for a vendor you will be ahead to specify an Amperage requirement - and the power needs for future projects should be included in this estimate (unless this cell will be dedicated to just one component for a long production run.)

And, I might be inclined to recommend a different process but can not offer specifics since the information involves a proprietary process.

Wish I could be more help.