You may want, or at least be thinking of, the annualized method described in Pub 505 http://www.irs.gov/publications/p505/ch02.html#en_US_2015_publink1000194669 (also downloadable in PDF) and referred to in Why are estimated taxes due "early" for the 2nd and 3rd quarters only? .
This doesn't prorate your payments as such; instead you use your income and deductions etc for each of the 3,2,3,4-month "quarters" to compute a prorated tax for the partial year, and pay the excess over the amount already paid. If your income etc amounts are (nearly) the same each month, then this computation will result in payments that are 3,2,3,4/12ths of 90% of your whole-year tax, but not if your amounts vary over the year.
If you do use this method (and benefit from it) you MUST file form 2210 schedule AI with your return next filing season to demonstrate that your quarterly computations, and payments, met the requirements. You need to keep good per-period (or per-month) records of all tax-relevant amounts, and don't even try to do this form by hand, it'll drive you nuts; use software or a professional preparer (who also uses software), but I'd expect someone in your situation probably needs to do one of those anyway.
But partnership puts a wrinkle on this. As a partner, your taxable income and expense is not necessarily the cash you receive or pay; it is your allocated share of the partnership's income and expenses, whether or not they are distributed to you. A partnership to operate a business (like lawyers, as opposed to an investment partnership) probably distributes the allocated amounts, at least approximately, rather than holding them in the partnership; I expect this is your year-end draw (technically a draw can be any allowed amount, not necessarily the allocated amount). In other words, your husband does earn this money during the year, he just receives it at the end.
If the year-end distribution (or allocation if different) is significant (say more than 5% of your total income) and the partnership is not tracking and reporting these amounts (promptly!) for the IRS quarters -- and I suspect that's what they were telling you "affects other partners" -- you won't have the data to correctly compute your "quarterly" taxes, and may thus subject yourself to penalty for not timely paying enough. If the amount is reasonably predictable you can probably get away with using a conservative (high-side) guess to compute your payments, and then divide the actual full-year amounts on your K-1 over 12 months for 2210-AI; this won't be exactly correct, but unless the partnership business is highly seasonal or volatile it will be close enough the IRS won't waste its time on you.
PS- the "quarters" are much closer to 13,9,13,17 weeks. But it's months that matter.