Question

[Eli51]

If my wife Sponsors me & she signs the undertaking to Sponsor me could my ex wife come after her for child support even though my ex has sole custody?

 

[Bs65]

Others can comment but sounds like for something so critical you need to ask a lawyer not a public immigration forum. Only guessing but would have thought immigration undertakings are completely separate from child support obligations but only a lawyer could say for sure.

 

[vensak]

not directly.
Responsibilities of your current wife are only her dependants (which your child is not).
But following can happen. Your ex can still ask for money for child from you, which might result you ending up on a social support. And your current wife if responsible for you ending up on social support and pay up for that.