Realistically, the only reason you'd need to have the mobile connector with you is if you intend to plug in at your destination, like a friend's house. I'm going to visit my parents next week and plan to bring my MC with me so I can plug into their 110 outlet in the garage, mainly just to see how much charge I get overnight. Haven't used a 110 yet, as I have the 14-50 outlet here at home.
Not sure on MY, but on my MX, it's about 1% per hour. I took my mc when I took a trip in 2019. It came in handy at my BiL's house, as well as a hotel we stayed at that didn't have a destination charger. It was either pick a hotel that had a charger, or stay at a place that was closer to where we wanted to be.
I took an extension cord that was rated for this, along with a triple tap, in case the only outlet within reach was already in use.
It wasn't fast, but it certainly got us through the trip.
Fwiw, I used the mc on 110v for the last three years, and as long as I was always plugged in, it was fine for the around town stuff.
The only "problem" is that it can never get me to 100% before a trip. So I'd just account for leaving home at 90% and plan charging accordingly.
YMMV, obviously, but bring a good extension cord along w the MC.