@Brandon9000,
Kicking his dog is an impeachable offense if a simple majority in the house deems it as such. We would hope that the Senate would summarily dispense with such a charge, but the president would still have been impeached.
Neither of the individuals of whom you've asked this question needs to come up with a clearly criminal act that can be proven which is why Mueller's report provides all the ammo the Democrats need to impeach Trump.
Pelosi knows that in all probability she could have the president impeached. She has the necessary majority and could if she wanted, likely whip up the necessary votes to push it through.
She's not resisting the calls of the firebrands because she doesn't think she can prove an impeachable offense has been committed, she wouldn't have to. She's resisting because of the political implications of impeaching Trump.
She knows with 99.9999% certainty that the Senate would acquit him and the blowback against her and the Dems would be the same as it was against Gingrich and the GOP when they impeached Clinton.
It would be a very interesting matter if the Dems had the 2/3rds of the Senate necessary to convict the president, because there would be some political gain from removing the GOP's 2020 candidate from the race with only a few months to go before the election, but we'll never know how low the Dems are willing to go (in this case) because the votes are not there.