Actually, I don't think it's that much of a problem.
In Dublin, there has been an improvement in Probate times - currently about 12 weeks, less if the matter can be expedited, because of signed Contracts. And I'd rather assume that both Probates can go in tandem, rather than consecutively.
If the Contracts are signed, then both sides are tied in. And, again, I'd rather assume that the Vendors want the sale to go through so they are unlikely to sit on it.
The Executors can sign Contracts even if Probate has not issued.
Above all else, talk this through with your own solicitor - on here we can only speculate without knowing the full facts specific to the OP's circumstances.
mf