They are both going to be removed. This fact sheet
https://consultations.tfl.gov.uk/crossrail2/october2015/user_uploads/sw1.pdf
says:
"The proposed increase to train services mean it is likely that a small number of existing level crossings in the area would need to be removed to increase safety and improve local road connectivity. This could include both the level crossings on West Barnes Lane near Motspur Park station, and Elm Road near New Malden.
Network Rail will work closely with local communities and the local authority to find an appropriate resolution for each crossing. This could mean access across the railway is provided by a bridge or an underpass, or via a diversion around the railway.
We are still at a very early stage in the development of our proposals for Crossrail 2 and the process to understand the work that we need to carry out at the level crossings along the route has not yet started.
When our plans are further developed we will carry out further consultation in the local areas about the potential impacts of closing any level crossings. However, we would welcome early input from the local community as part
of this consultation."
The response to the consultation can be found here:
https://consultations.tfl.gov.uk/cr..._uploads/crossrail2autumn2015consultation.pdf
I won't paste the relevant bit re the level crossings (pages 79/80) but there was more support for closing them than keeping them open.