Can also recommend this approach - it's how we've got 2 children plus a load of stuff to Scotland several years running. To Arran this exact way last year. I camped overnight somewhere in the borders, then met family at the ferry terminal station. It's obviously not the cheapest option, but is best for preserving everyone's sanity while still taking bags, bikes, etc.
Ardrossan wouldn't be too painful a drive to do in one go if you started early.
While I'm in the car thread - any biggish estate recommendations for a budget of 5-10K? Must be ULEZ compliant and comfortable (I have a bad back). Sold our previous car and realising not having one is a massive pain. Was looking for a late 2000s V70 but there aren't many non-diesel ones around and we have to get something before Easter so probably need to widen the search. Would sort of like a 5 series due to having a bmw before and liking it, but suspect this would end up horribly expensive to keep going.