You current extension will still be valid since you are extending it for 60 days to visit your child. You can apply for the new extension near the end of the 60 days.
This from clause 2.18 the immigration order.
(5) In the case of parents, the father or mother must maintain an average annual income of no less than Baht 40,000 per month throughout the year or must have deposited funds of no less than Baht 400,000 to cover expenses for one year.
No mention of the 2 months. Only number 6 mentions the 2 months for a extension based upon marriage.
Download: Immigration Order 327/2557 (2014)