I’d beg to differ.
OP has no doubt suffered a lifetime of emotional abuse and coercive control from her mother. It wouldn’t have started just now when she’s an adult.
She will have been groomed by her mother since childhood into accepting this behaviour, and fearing the consequences if she challenges her authority; these kind of patterns are not easy to break and you are essentially victim blaming with what you’re saying here. Far from OP “letting” her mother control her, it will have started when OP had absolutely no power over the situation at all, and will have been normalised over years, decades even.
OP, I agree with pp that finding alternative childcare must be an absolute priority for you. Apart from anything else, someone who’s this level of controlling (and she is extremely controlling) will damage your DC too. I don’t suppose this will be easy financially but you really need to explore every other option. Far more urgently than sorting out the scratched up wallpaper, in fact!
Her continuing to do it is giving her the power to continue to control and emotionally abuse you. Threatening to withdraw the childcare that enables you to work is a dreadful thing to do, and shows no love or care for either you or your DC. Which again is why you need to stop entrusting your DC to her.
You need to know this isn’t normal, not remotely. As you say, it’s your house that you’ve paid for, and you get the choose the decor - your reason here is perfectly sound but the fact it’s your home means it can be for any reason you choose! And she should have no say in it whatsoever. Let her put that wallpaper up in her own home if she loves it so much.
And you need to get some support around breaking away from your controlling mother. If affording counselling or similar is an issue, you might be able to get some support via your GP or from a free service local to you (they’re rare, but they do exist). Or you could post on the Stately Homes thread, or start your own thread on the Relationships board - or just get this one moved to Relationships.
One of the biggest strengths of MN is that there is an army of women here who’ve experienced coercive control/emotional abuse from parents and/or partners and so there’s a huge amount of collective understanding and wisdom around these issues. So many women have been empowered to leave abusive partners or stand up to abusive parents (coercive control is recognised in law as a form of abuse), with support from other women here.
Good luck.