See, I am so used to the bad weather here that I am used to camping in the rain. Especially for Cub camp - that's at least a 50% chance of rain when packing up and also at least 1 of 2 nights every June. And as the hostel we use in March has limited space (we officially just all fit, but the mix of boys and girls means sometimes not enough rooms for the leaders - and it's a choice of the 3 men or 1 woman taking the 1 room available...so I often end up in my tent outside).
I have a rug, or sometimes just a flattened cardboard box, inside the door and all shoes/boots come off there to stop tracking mud further in. Rain gear comes off there and I hang them dripping onto mat.
I keep a full change of clothes (knickers and bra included), dry shoes and a towel in a bag under the front seat for when packing up is done to drive home in dry things.
But you have to embrace it. I love the sound of the rain on the roof, so different and calming compared to the usual sirens etc. Bring a good book always and a book of sudoku puzzles for peaceful time. A board game and deck of cards for family enjoyment.
I will admit I bought a new tent a couple of years ago with a porch to have cover to cook in on rainy days. That made a big positive difference. And a good sleeping set up so you are well rested also really helps being able to deal with whatever weather and other difficulties that might happen.