Vizla / Weimaraner seem to make good distance running dogs. Mine is a German Shepherd / Husky / Retriever cross and he is a bit too big and heavy for my normal 6min km pace, he starts eating grass and throwing up at about 10k. Also cannot resist a squirrel so has to be on a lead for running because he can and does catch them, deadly clever rather than fast. I use him for when I should be taking it easy, we can go and pootle for a couple of hours.
Take the run you want to do most, whether that is for the charity you prefer or the race you'd rather do. Then tell the other charity, don't worry they will have more people to take the place. And they are more likely to give you another place next year for being sensible.
I'm a charity fundraiser and yes I do get paid for that. We have to pay quite a lot for places and the number we can get is often restricted, so we only have five VLM places while we have many more potential runners. We have learned the hard way, I am very worried about the Royal Parks Half team, they don't seem to have raised anything and they didn't fill in the entry forms until literally the last possible hour, or people not running and not telling us so we can transfer the place (one company asked for more British 10k places than they used but we still had to pay £35 for the unused entries, another had a VLM drop out and didn't tell us in time to defer or replace). So from now on we're going to have to charge a registration fee which is a shame. As a runner myself I know there is a limit to how much money one can raise anyway and enter all my races on my own place.
Can you get a treatment scotty, osteo, Physio whatever? They'll tell you what to do and do listen. My colleague was out for ages with groin but she didn't rest it at first. If yours is bad then not doing the race is much better than months on the bench.