I'm going to Hawaii in mid-July and would love to get in the best shape I can by then to look good in a swimsuit!

But I'm confused on what's best to do between now and then. I'm 5'4 and 115-117 lbs with a very small build, and a pear shape so most of my weight is in my legs and hips. I've been 110 for years and felt great at that weight but haven't been able to lose the 5-6 lbs since having my second child almost three years ago

I also haven't been able to consistently work out all this time so I feel I also lost muscle and gained fat so I look skinny fat and wider than I'd like.
Now I've started lifting again and hoping I'll be able to keep with it consistently, but I'm confused on how to eat. MFP estimates my TDEE at 1520 but I believe it's closer to 1400 as that's around how much I've been eating on average and maintaining on. My first instinct is to try and lose those five pesky lbs, but to lose .5 lb a week I need to eat 1260, which I can do but I don't know if eating that little and trying to lift can even work? Will I be able to build any muscle? I also have trouble getting enough protein, my diet is pretty carb-heavy and getting even .8 g per lb of protein on a 1200-1300 calorie diet leaves very little room for carbs! But I'm afraid if I stay at maintenance, I won't lose any fat by then and it'll just be covering up any muscle and make me look bigger. Thoughts??
A few notes: portion size and satiety are absolutely not an issue for me, I have some stomach issues and get full very quickly and have often gone days without realizing I've forgotten to eat till late in the evening, but I have trouble eating the 'right' things and giving up foods entirely. So I'm willing to go as low as needed calorie-wise but at this point absolutely not willing to try anything like low-carb, and I also despise cardio and HIIT makes me feel really ill, so I'd like to avoid it if possible and just stick to lifting. Any advice within these boundaries would be most welcome! I'm obviously not counting on looking like a fitness model by July, just whittling away as much fat as possible while still looking somewhat toned would be great.