If you’re using Mailchimp for business and can provide them with evidence that you are a business (the most common requirement is that you provide them with your VAT number) then they should not be charging you VAT under VATMOSS rules. They should not be charging VAT at all, but instead you would account for VAT a under the reverse charge process.
For the UK it's not that hard to do yourself, to be honest, if you can read carefully and are proficient with spreadsheets. I only do UK but I guess the difficulty with other EU countries would be the language barrier.