Hustle might work as an alternative to the violent implications of shoved, :
1 [WITH OBJECT] Push roughly; jostle:
they were hissed and hustled as
they went in
1.1 [WITH OBJECT AND ADVERBIAL OF DIRECTION] Force (someone) to move hurriedly or unceremoniously:
I was hustled away to a cold cell
1.2 [NO OBJECT, WITH ADVERBIAL OF DIRECTION] Push one’s way; bustle:
Stockwell hustled into the penalty area
2 [WITH OBJECT] informal , chiefly North American Obtain illicitly or
by forceful action:
Linda hustled money from men she met
2.1 (hustle someone into) Pressure someone into doing something:
don’t be hustled into anything unless you really want to
Although both hustle and shove can denote the same sense of pushing, hustle can also connote a less violent compulsion. The context of the OP leaves the interpretation open, but welcomes the "gentler" sense of hurried pressure:
The man was hustled towards the department store by his enthusiastic spouse.
The definition of shove is pretty straightforward:
1.0 Push (someone or something) roughly:
police started pushing and shoving people down the street
[NO OBJECT]: kids pushed, kicked, and shoved
1.1 [NO OBJECT, WITH ADVERBIAL OF DIRECTION] Make one’s way by pushing someone or something:
Woolley shoved past him
The operational definition of the OP is actually violent:
1.0 Using or involving physical force intended to hurt, damage, or kill
someone or something:
a violent confrontation with riot police
1.1 Law Involving an unlawful exercise or exhibition of force.
At a strictly interpersonal level, it would not be violence if there was no intent to harm, but there can always be two interpretations of intent. The person shoving interprets their own intentions objectively, while the one being shoved interprets those intentions subjectively. The legal definition comes into play when the person being shoved feels violated enough to ask the police to intervene. Even then the police may just show up to cool things down.
There is no legal violence in shoving if both parties agreed to rough each other up--including a gradual escalation in conflict. The players in a rugby or American football game, are often shoving each other violently, but the participants find some pleasure in exchanging these harmful actions to test their mettle. In ice hockey players can actually have a grand fist fight, while the spectators cheer them on, but they each spend 5 minutes in the penalty box as a token nod to the fact that we still disapprove of violence in general.
In the context of the OP, the connotations would be a matter of divergent opinion. Was the action of shoving actually harmful? Does the woman intend to violate the man's freedom, dignity or physical wellbeing? Does the man feel violated? Have they agreed to enjoy this shoving process on the way to the store? The interpretation of any third party would be highly subjective.