Do you have to remove existing grass to rotivate?

I am hoping for some help from some experienced gardeners and would be grateful of any advice... please.
Our garden has really poor drainage and when it rains it just pools and then turns into a muddy mess!! That along with 2 dogs that like to run around the garden means the lawn is not what you could call a lawn.
I have looked into drainage and we are going to sort that out.
Now here is the problem. We are working on a very tiny budget and were planning on doing most of the work ourselves, but I am pregnant and my boyfriend has a hernia so the tough work we were planning to do, we cant - especially not before the summer is over.
So we plan to sort the drainage out, then rotivate the soil and level it off.
But the question is -
Do we have remove the existing lawn before we rotivate it???
We are planning on laying a weed barrier and then laying artificial grass after doing so. As we just want a simple garden with little maintenance!!
I think we should be able to just rotivate it as we are laying a weed barrier so it shouldnt make a difference what is underneath, but my boyfriend thinks we need to remove the existing grass first. (Which I think is going to increase what we are having to pay out!!).
Thanks so much in advance for any replies or advice!!
Sharron x

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