my 3 year old and his dirty protests

[Velvian]

My DS turned 3 in July is constantly weeing on the carpet and sofas when he is at home, (he also poos occasionally). This weekend I covered the sofas with bed mats & then blankets to protect them. Yesterday, when at home with DH, he pulled back the blanket then the sheet, sat on the sofa and peed.

He is DC3 (so should know what I'm doing ;D), he has perfect bladder control & never has accidents out or at nursery. He loves being naughty and is a real show off. I've tried ignoring it & cleaning up without interaction, I've tried talking to him about what he should be doing and I've tried treats for using the toilet.
Any suggestions?

Is he getting enough exercise? Could he be bored and looking for excitement? Does he get out daily for physical play?

Definitely looking for excitement. He goes out on his scooter for 10/15 (one way) trips to school at least one school run & usually both. Usually 1 trip to a park & access to the garden when we are in the house. The trouble is I'm only at home with him on Thursdays and Fridays and part of Wednesday morning and I have tons of washing & tidying etc by this point. I think if I was constantly entertaining him it wouldn't be an issue

Could he go to nursery?

Yes he could, we are only using 6 of his free hours, this afternoon & tomorrow afternoon, but he is with a nanny & grandparents at other times, so we only get 1 day & 2 part mornings at home together. It worked well with DS1 & DD to have some time at home 1 or twice a week, without needing to constantly entertain or "parent" Thanks Violet, talking it through makes me realise that I only have the next school year with him & the housework may have to slide while I make the most of him (at least there would be less wee to clean).

Yes...there's always housework but not always a toddler in the house.