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Here you go:

If your husband (if he is the employee with EP and you are a DP holder), and his fixed salary or basic salary  is above S$10k per month then he can apply Long term visit pass for your mother and she can stay more than 89 days.

If salary is less than 10k, then please apply a visit visa for her at her place (check the local tour operator) and your husband can write a mail using office mail stating that she will be visiting here to see her pregnant daughter. The travel operator can print out the page and attached with application and submit with other necessary documents ( check with the travel operator) to get visa approval (normally she will get 1year visa, if she is older more than 60 yrs then will get 3 months).

On her arrival she will get 30 days stay period, once she arrives apply in 15 days online to extend to another 30 days (total 59 days) which you can apply online. If you want to extend 60 days (total 89 days), then visit ICA office to apply there. Details are as follow:

Hi,
Surya
I am pleased to hear from you. Thank you so much for
Your reply with all the detalis. This is highly appreciated
My husband have hold WP(Work Permit) in this case wouldnt be any problem to apply for long term pass. And his salary above 5k.

Read again I said he can apply long term pass for parents only if his fixed or basic salary is above 10k ( not 5k what you have mentioned). 5k is the benchmark to apply for dependent pass or in other way he can bring his spouse or family. He must be holding Employment Pass (EP) not Work pass which is meant for labour or foreign workers.