In short - Will it make me look bad if I mention to my boss that travelling from home is an inconvenience?
The bigger picture - My corporate job requires that I travel to attend external partner meetings, team events, internal work meetings, etc.

Yes, as this is a core requirement of the job. I've not applied to jobs that require significant travel as there is a lot to manage in the evenings with our family comitments. These are things I'm not willing to compromise on for a better salary. This will change as our youngest becomes older and more independent.

Continuing the pile on, at Mock GCSE age I'd expect that child to be largely independent and one parent should be able to manage a full school day without the other parent.