You could use pull-ups to go out, present them as big girl pants. Or use the washable training pants (waterproof outer with towelling lining) and boost their absorbency with a microfibre cloth folded into a pad.
Go with the potty she likes. Dolly or teddy can sit on the cheapy at the same time. Potette very useful, you can make your own liners which are cheaper from pedal bin liners and something absorbent like value sanitary pads or a few sheets of kitchen roll folded into a pad.
You could have a small washing up bowl or large ice-cream tub with water and a small squirt of baby wash in it for dd to wash hands after each potty use, and of course a towel. You don't need to drag her off to wash hands and you can leave the water for a few washes before changing it.
Use loo roll, keep one with your washing hands kit. Save wipes for messy clean-ups.
To get dd to sit a bit longer, sit dolly/teddy on the cheap potty at the same time as dd and say she can get up when teddy/dolly does. Or have some toys and books to occupy while sitting. Using the potty is a novelty at the moment, but the number of wees she does will reduce as she does bigger ones less often.
I think you just have to go for it on outings, if you will be mostly outside, just take a lot of clothes to change and the potty. If inside, the trainer pants with microfibre cloth should help with the mess. Potty her before you go into a supermarket for example and at some point during ( leave your trolley at customer services if necessary) or go with someone else so you can just dash to the loo with dd.
I doubt it will be months at dd's present rate of progress.
Yes, there will be mess and accidents from time to time, but that's the reality of toilet training and you just have to accept it. In fact, that's the reality of having children full stop!