My cousin moved to France with her kids and within 6 months after starting school, the 9/10 year old was chatting away in French and keeping up at school.
This child will never quite be a 'native' French speaker, I don't think, but immersion does take you far.
However without immersion, so, short of you packing up and moving to a Spanish speaking place, at age 9 a child won't usually learn a language without actual work/effort. I believe the time for that is up to about age 5. From age 5 we stop learning/developing language (our native language included) purely from being 'a bit' exposed to it, and start learning/developing through explicit instruction/reading/conscious effort instead. If we are monolingual up to age 5, we might become very proficient in another language but will never become properly bilingual (two 'native' languages).
So particularly with your 9yo I don't think simply starting to speak to her in Spanish is a good strategy - as you say, she'd probably become annoyed!
However, if she is keen, you could do something like Duolingo with her. My DS has been learning French with Duolingo. He does about 5 minutes every day. It is amazing how much progress he is making; the 'little and often' approach really, really works.
In order for this to work, I think you need to discuss it with your DD and come to a joint decision. My DS really wanted to learn French and so I explained to him that you can dabble around a bit with a language and have some fun, but if you want to really learn it, you will need to put some effort into it very regularly. He chose to do that, rather than just explore the language a bit. So we kind of made a contract, he wants to put in the effort so it is not me making him do it, but I can remind him and occasionally nag him to do it if necessary to help keep him on track because overall that IS what he wants, even if sometimes he doesn't feel like it. In turn, we signed him up for French club at school for some interactive practice, and support him with his Duolingo sessions at home (we both speak French as a learned language). Being closely involved means that we know where he currently is at with his learning, so in addition to the 5 minutes formal learning we can point out relevant French stuff in the environment (e.g. when knowing the French word for something helps with understanding the spelling/pronounciation of an English word).
I really think at age 9 it needs to be your child's 'informed' decision, so she needs to know that it will entail continuous effort and still choose to do it.
Good luck! It has been a joy for me to see my DS making such progress with French. I hope your DD will be well motivated by the benefits Spanish can give her (understanding your TV programme, but also when you visit relatives in Spanish speaking places... how good is it to be able to understand what's going on?!) and choose to put the effort in.