The arrangement that fails is the one nobody defined. A business hires somebody for advertising and somebody else for the website, and then discovers that the advertising person wants changes to pages the website person maintains. Neither is wrong, both are doing what they were engaged to do, and the owner spends their week arbitrating between two people who have never spoken.
Draw the boundary by outcome rather than by task, which is what prevents most of that. One provider owns the website and everything on it. Another owns the advertising and the reporting. Whoever needs a change on the other side requests it through you or directly, with the ownership unambiguous. Splitting by task instead produces overlaps at every seam.
Introduce them to each other rather than routing everything through yourself, because you become the bottleneck otherwise. Two competent providers who can speak directly resolve in a message what would otherwise take three exchanges with you in the middle translating imperfectly. Say plainly that they are expected to coordinate, and that neither reports to the other.
Keep the accounts in your name with both granted access, which is the arrangement that makes any of this possible. If one provider controls the analytics property and the other cannot see it, the second is working without evidence. Shared access to the accounts you own removes most of the friction that multi provider arrangements produce.
Decide who is accountable for the outcome, since two providers each doing their part well can still produce a result nobody owns. If enquiries are flat, somebody should be responsible for working out why, and if that is nobody it will be you. Naming it in advance is better than discovering the gap during a quiet quarter.
Be careful about asking one provider to evaluate another, which happens naturally and is rarely useful. Everybody believes their own discipline is where the problem sits, and a website person asked about advertising performance will find website reasons. If you want an independent view, pay somebody with no stake for a few hours.
Watch for the situation where the arrangement exists because nobody wanted a difficult conversation. Businesses occasionally add a second provider rather than addressing a problem with the first, and then carry both costs indefinitely. That is a different situation from a genuine split, and it is worth being honest about which one you are in.
Then review it annually against whether the split still makes sense. As a business grows, the sensible boundaries move, and an arrangement designed when the site was five pages may not suit one with two hundred.
Agree how disagreements get resolved before they arise, since two competent providers will occasionally recommend opposite things and somebody has to decide. Naming that the decision is yours, informed by both, prevents the situation where each waits for the other to concede while nothing progresses.
Watch what the arrangement costs in your attention rather than only in fees, because coordination is the hidden expense. Two providers producing separate reports, separate invoices, and separate questions consume more of your week than one, and that cost is worth counting when deciding whether the split is genuinely necessary.
Review the arrangement when either provider changes, since a split designed around two specific people does not automatically survive a replacement. The boundaries that worked with one set of skills frequently need redrawing with another.