Techniques to extract lipids
Casein is a mixture of phosphoproteins found in milk that accounts for approximately 80% of the total protein content of cow milk (cow milk contains 3.3% total protein). Hence, it is easy to prepare casein as a pure protein from cow milk. 

Casein exists in milk as the water soluble calcium salt of a phosphoprotein (UC, Davis). Thus, it is usually prepared by acid precipitation. Acid treatment removes the calcium cation, leaving a water insoluble phosphoprotein. Note that casein is amphoteric, i.e., it forms salts with both acids and alkalines.

Generally, acetic acid is used in the casein precipitation, because its mildness and less harsh property compared to hydrochloric acid. Although, most people extract casein precipitation in the cold acid solutions, such practice would lead to the formation of protein with poor physical properties. Softness and rather incomplete separation of the casein are problems encountered.

If the precipitation is performed in warm solutions, the casein separates as a single large colloid, with complete separation, leaving a yellow solution of whey behind (which primarily consists of milk-sugar, lactose).

Keep in mind that usual casein precipitation is comparatively easy but delicate. If too much acid is added or if the acid is added too quickly, or if the acid is too strong, part of casein mass will redissolve in whey. Also, casein may be extracted from whole milk. Disadvantages are that whole milk contains a relatively large concentration of fat. This fat will be physically included in the casein curd as it separates. Thus, I'd recommend to use skim milk (if possible), which would be one solution for your co-precipitation of fat problem.

A procedure for casein precipitation in UC, Davis is as follows:

First, prepare a solution of $\pu{7.0 mL}$ glacial acetic acid in $\pu{50.0 mL}$ deionized water. This is your acid solution to be used for the precipitation. 

Place $\pu{600.0 mL}$ of skim milk in a $1$-$\mathrm{L}$ beaker. Warm the milk to $\pu{110 ^{\circ}F}$ (approximately $\pu{43 ^{\circ}C}$; Note that temperature should not be $\gt \pu{55 ^{\circ}C}$). At this temperature, add the acetic acid solution (prepared earlier) drop-wise and with stirring. At a certain point, casein will separate as an amorphous mass leaving clear supernatant (light yellowish). Gather the solid from the beaker with a glass stirring rod or separate it using suction filtration.

Caution: Do not add any more acid than necessary to obtain a good curd. A few minutes must be given between acid additions to allow for stabilization.

Press the removed mass of casein between paper tissues to remove as much water as possible. Place the mass of casein in a food blender with $\pu{500 mL}$ of water. Suspend the casein in the water by blending as much as possible.

Separate the casein from the water with a filter and wash the cake with 2-propanol. If 2-propanol is not available use ethanol or some low molecular weight alcohol.

Let the casein powder air dry. You may wash the dried cake with two portion of ether if necessary. You may suspend the dry powder in ether and let it soak well before filtering.

Yield of casein in $\pu{600.0 mL}$ of skim milk is reported as $\pu{13.8 g}$.