I have just seen this. He supposed to increase the child transaction fee, not the parent. Although, I am surprised that the parent (the first transaction) was unable to increase in fee. But how about increasing the child transaction fee. Probably that should work.
BIP125 says that:
3. The replacement transaction pays an absolute fee of at least the sum paid by the original transactions.
4. The replacement transaction must also pay for its own bandwidth at or above the rate set by the node's minimum relay fee setting. For example, if the minimum relay fee is 1 satoshi/byte and the replacement transaction is 500 bytes total, then the replacement must pay a fee at least 500 satoshis higher than the sum of the originals.
The thing I am not sure about is what exactly "
original transactions" refers to.
Does it mean the transactions that have the same input(s) as the replacing transaction or their unconfirmed children are also included?
Considering what happened to OP when trying to increase the fee, it seems that it's the latter.
If that's the case and OP wants to replace the first transaction with a new one, there are four transactions that must be removed from the mempool.
The absolute fee that is paid for the replacing transaction must be bigger than the total fee paid for those four transactions which is around 0.000039 BTC.
According to rule number 4, the replacing transaction must pay another ~140 satoshi too.
In the case my calculations are correct and OP wants to replace the first transaction with a new one, the replacing transaction must have the fee rate of around 30 sat/vbyte.