I'm not really sure what you're saying here. Which would resolve first? I mean, why wouldn't they resolve at the same time?
They can't, can they? As a reminder, this was about a Magic: The Gathering style optional mulligan being added in... which I take to include the same penalty (shuffle your hand back into your deck, draw a new one that is one card smaller). Either we end up with something way to forgiving for an optional mulligan, or way too punishing.
If you allow someone to play down their opening Active Pokémon before shuffling away and redrawing the rest of their opening hand, that ain't a mulligan. I'll refer to it as a mini-mulligan when I come back to it, but onto the problems of trying to resolve the optional and mandatory mulligans.
If the mandatory mulligans are resolved first then... what happens if someone's optional mulligan results in an opening hand with no Pokémon? There are ways to handle this by adding even more rules... but were adding even more rules.
If the Optional happens first, and the -1 card penalty per attempt applies to the mandatory mulligan as well, we get to a point where a lot of time is lost as that player gets down to a small hand with low odds of getting an opening Pokémon... maybe even just trying to topdeck one because they're down to one-card hand! @_@ It might be funny, but for tournament play that much of a time sink is a problem. It makes the optional mulligan far too risky.
If the Optional happens first but the -1 card penalty per attempt is waved if the player has to take a mandatory mulligan, players are free to try for that perfect opening hand, and if they whiff, they just have to take their hand down to one card (via Optional mulligans) and hope to whiff on a Pokémon, forcing a mandatory mulligan that resets them to a seven card hand (even if they're finally stuck with one as soon as it hits a basic).
If we allow a "mini-mulligan", that just doesn't lend itself well to the nature of the Pokémon TCG. Decks that can afford to run more Oranguru (SUM) and easily "consumed" Item cards (like Nest Ball) can a serioous edge, milking the mini-mulligan because they'll just draw/search with what few cards they get on a "bad" hand, while a good hand lets them get a great setup! No, I don't mean there is a 50-50 chance of one or the other, I just mean decks which can conform to this are getting a disproportionate reward relative to the risk.
Yes, yes... I may have missed some obvious solution; let me know if I did.
If you do not have Private Messages enabled, it really limits you in discussing the Pokémon TCG.