I would never "gift" (even with the various suggestions already made of ring-fencing that sum somehow) large sums of money to a close relative unless I could truly afford to say goodbye to that money - either permanently, or for an indefinite period of time.
That'd mean that I'd have to have such huge savings that the disppearance of said amount would have no impact upon me & my immediate family, even if all sorts of unforseen circumstances befell us. Not many people are in such a secure position. You can never tell what's round the corner, and MIL needs to be told very firmly that you will not be able to "help".
Unless she has access to all your accounts & payslips, she cannot possibly know what your household income is, what your liabilities are, or indeed what plans you have for the future, and I think it's appalling that she should pressurise DP to do such a thing, based, presumably, on assumptions about your "wealth" gleaned (probably) from what she thinks he earns, what car he drives or what sort of house you live in. After all, if DP was able, and more importantly, wanted to help his sister, he wouldn't wait until he was asked would he !
Even assuming that he could literally "throw" a sum away, irrespective of what the future might bring (illness, accident, redundancy etc) I would not consider "helping" someone unless they themselves had already done everything possible to help themselves. This SIL must be in her late 20s, early 30s (??) and has only just got her first job ..... and it's part time !!! Okay ..... I know that even with "good" jobs, it's damn difficult to buy these days, but she has basically dossed about for 10 years by the sounds of it and isn't making any effort to improve her buying position by maximising her income opportunities. If that's her attitude, what would happen once (if) DH gets involved and she's then made redundant, or sacked, ..... would MIL then pressure DP to pick up the slack again ?
COV, I think you need to be very firm with DH over this if he's at all wavering. If he goes ahead, the resentment you'd feel - even if, at the moment, you could nominally "afford" to "help" - at paying out for a lazy scrounger (well, she is isn't she ?) could seriously affect your own relationship. I also suspect you'd feel furious at MIL, and at DH's rolling over at her command .... and that wouldn't be healthy for anyone.