I think that’s a good plan - just stop asking her to say words and get your family to stop too.
So Like this
“ do you want juice or milk? “
She indicates juice .
“ So you’d like juice. Good, we have black currant juice today, your favourite . Do you want to help pour it out ? “
“ Do you want the red cup or the green cup? “ ( you show them as obviously she doesn’t know the names of colours ).
She points to green.
“ you want the green cup with handles. Does teddy want a drink too? “
She nods
You pretend to give a drink to teddy etc .
You DONT try to get her to reply to you in words, or not give her what she wants until she says it.
The most important thing is not that she talks but that you can she she understands what YOU are saying. If she can HEAR the difference between juice / milk ( rather than recognise the bottles ) that indicates ( not proof ) that her hearing and comprehension are ok .
If you say “ do you what to go into the garden ? “ and she runs to get her coat / to the door, you know she links these activities ( wearing a coat to go outside ).
So If you are playing with her with blocks, talk about what she is doing .
“ oh shall we make a big tower? Do you want to put on another block? Oh you have two blocks , well done. “
“ oh now you have knocked them all down - crash ! “ .
DON’T say “ Here’s a block - what is it? No say the word block. Good now say the word please.”
Etc etc.
If she says a word wrongly DONT correct her EVER. Just model the correct word.
So if she points to a cat and says “ dog”, just say “ yes that’s a cat, it’s Mog who lives next door. The cat says Miao . Do you want to pat her ? “
Some children just hate being asked to perform, so pressurising her to do it more won’t work and may be making her anxious.
If she is stubborn as you say, the last thing you want to do is get into a control battle about this. Her speaking or not is not under your control so don’t even go there.
I’d also speak to your health visitor to get her advice, in case she needs SAL assessment.