The actress was spotted being a good mom Tuesday on the heels of reports she upset the family by allegedly getting rid of the family pooch, Gordon, to spend more time with Harry Styles.

Olivia was having what appeared to be an emotional goodbye with her two children, Otis and Daisy, making sure to shower them with hugs and kisses before they climbed into a waiting limo.

The kids were traveling with backpacks and luggage ... which is interesting because their father, Jason Sudeikis, is across the pond in London.

As you know ... Olivia and Jason's ex-nanny is continuing to make nasty allegations against the estranged couple, even though they teamed up to call the nanny a liar. The latest salvo included claims Olivia gave up her dog within weeks of meeting Harry, allegedly so she could free up time to spend with the singer.

The nanny also claims Jason once told her Olivia only had the pup to keep up appearances and rarely looked after the pooch.