、、。
Pushing a small cart with a teapot and tea set on it, Seika came into the room.
Literal
Pot [and-と] tea-set [subj-が] was-on, small cart [obj-を] push-[and-て], Seika-[affectionate-ちゃん] [subj-が] room [to-に] entered-came.
Two stacked relative clauses feeding into one main verb of arrival: [ポットとティーセットが乗った] modifies カート, then 小さなカートを押して (the te-form) chains into 入ってきた. 乗る with things on a surface means 'to be resting on'; the past 乗った reads as 'that was on.' ~ちゃん is the affectionate/diminutive suffix typical for children, pets, or close friends. 入ってくる 'come in (toward the speaker/observer)' is the spatial-motion sense of the ~てくる auxiliary.