Garage is part of the house same as porch or patio or deck etc Typically no one wants exes walking uninvited in their garage either. If you don’t think garage is part of the house, then would it be ok for strangers to take stuff from you garage too?

Next time you could wait for mom outside with garage door closed. Why does it even need to be open if you don’t drive?

Yes I imagine dad will be mad about it. Anyone would. But he shouldn’t be mad at you. The only thing you could differently is keep garage door close. Otherwise I don’t see what else you could do if mom just goes in and takes stuff.